-
FRACTIONS Numerator- Denominator:
A fraction is just a shorthand way of expressing a division
problem. In other words, 5/2 = 5 2. The Numerator is
the top number in a fraction and the Denominator is
the bottom number. For example: 5/2, the 5 is the
numerator and the 2 is the denominator.
When adding and subtracting fractions, the
denominators of the fractions must be the same. If the
denominators of the fractions are already alike, just add
or subtract the numerators and put the result over the
common denominator. For example,
11
12+
5
12
1
12=
11 + 5 1
12=
15
12
If the denominators of the fractions are different,
multiply the fraction (S) by the fractional form (S) of the
number I which makes the denominators the same. For
example,
3
4+
5
3=
3
4(
3
3) +
5
3(
4
4) =
9
12+
20
12=
29
12
Since 12 is the lowest common denominator of 3 and 4,
then we had to multiply by 3/3 and 4/4 to get 12 in both
denominators. Since 3/3 and 4/4 both equal 1, we are
not changing the value of the fractions. 1 is the only
number you can multiply by without changing the value
sof the fractions.
When multiplying fractions, simply multiply the
numerators and multiply the denominators;; then
reduce. Reducing fractions is discussed below. For
example, (5/7)*(2/3) = 10/21. When one fraction is
multiplied by another fraction, the product is smaller
than either of the original fractions.
When dividing fractions, invert (put the denominator
over the numerator) the second fraction and multiply.
For example, (5/7) (1/3) = (5/7)*(3/1) = (5*3) / (7*1) =
15/7.
The Admission Test may include problems in which the
numerator or denominator itself is a fraction such as 5/
(2/3). Just remember this is just another notation for
division. For example, 5 (2/3) = 5 * (3/2) = (5/1)*(3/2)
= 15/2.
When adding, subtracting, multiplying and dividing
fractions, you must make sure the final fraction is in
reduced form, especially if your final answer does not
appear in the answer choices. Consider the example we
used when discussing adding and subtracting fractions.
The answer we got was 15/12. This answer would
probably not appear as one of the answer choices for
that question on the ADMISSION TEST because this
fraction is not reduced. To reduce a fraction, simply
factor the numerator and denominator into prime
factors and cancel out like factors: 15/12 = (3*5)/ 2*2*3
= 5/ (2*2) = 5/4.
Another way to tackle this problem is to just divide the
numerator and the denominator by the largest factor
that is common to both which in this example would be
3. The result would be 5/4.
A mixed number is a fractional number is ADMISSION
TEST greater than 1 which is expressed as a whole. In
most cases on the Admission Test, you will need to
convert number and a fraction such as 5/4 mixed
number to fractions by multiplying the denominator by
the whole number, adding this product to the
numerator, and putting this sum above the
denominator. For example, 53
4=
23
4
To convert a fraction in Admission Test greater than 1 to
a mixed number, divide the denominator into the
numerator to get the whole number and put the
remainder over the denominator to get the fractional
part. For example, 17/8 = 21
8
The Admission Test may ask you to compare fractions
and decide which one is larger or smaller. There are two
ways to compare fractions. One way is to find a common
denominator and multiply the fractions by the fractional
forms of 1 that give them the same denominator. For
example, suppose we want to know which fraction is
larger, 3/7 or 7/14? Since 14 is a common denominator,
multiply 3/7 by 2/2 to get 6/14. Clearly 7/14 is larger
than 6/14.
Another method for comparing fractions is cross-
multiplication. Consider the two fractions in the example
above, 3/7 and 7/14. In cross-multiplication, multiply the
denominator of each fraction by the numerator of the
opposite fraction; then compare the two products as
follows:
3
7
7
14
14*3 is 42 and 7*7 is 49. Since 49 is bigger than 42, 7/14
is bigger than 3/7. When Cross-multiplying you must be
careful to work from bottom to top in the direction of
the arrows. Had you multiplied numerator by
denominator working from top to bottom, you would
have gotten the wrong answer.
-
The following is an example of a Admission Test question
asking you to compare more than two fractions.
Example: Which of the following fractions is smaller?
To solve this type of problem, just compare the fractions
two at a time. First, compare 4/7 and 5/8 and eliminate
the largest of the two. The smaller of these two is 4/7.
Now compare 4/7 to 8/11. And eliminate the largest. The
smallest fraction is 4/7.
One reminder about fractions: If the denominators are
alike and the numerators are different, the one with the
largest numerator is the largest fractions; if the
numerators are alike and the denominators are
different, the one with the largest denominator is the
smallest fraction. For example, 11/13 is larger than
11/14. If both the numerators and the denominators are
different, you must use one of the methods described
above to determine which is larger.
Comparison of Fractions
If fractions A and B have the same denominator, and A
has a larger numerator, then fraction A is larger. (We are
assuming here, and for the rest of this refresher session,
that numerators and denominators are positive.)
Example: 56/271 is greater than 53/271 because the
numerator of the first fraction is greater than the
numerator of the second.
If fractions A and B have the same numerator and A has
a larger denominator then fraction A is smaller. Example:
37/256 is smaller than 37/254.
If fraction A has a larger numerator and a smaller
denominator than fraction B, then fraction A is larger
than B.
Example: 6/11 is larger than 4/13. (If this does seem
obvious, compare both fractions with 6/13).
EQUATION The basic principle to which you must adhere in
solving
any equation is that you can manipulate the equation
any way as you do the same thing to both sides. For
example, you may always add the same number to each
side, subtract the same or number from each side,
multiply or divide each side by the same number (except
0), square each root side, take the squarer of each side
(if the quantities are positive), of take the reciprocal of
each side. These comments apply to inequalities, as well,
but here you must be very careful because some
procedures, such as multiplying or dividing by a negative
number and taking reciprocals, reverse inequalities.
A typical BBA Admission Test several world problems,
covering almost every math topic for which you are
responsible. To solve world problems algebraically, you
must treat algebra as a foreign language and learn to
translate word for word from English into algebra, just
as you would from English into French or Spanish or any
other foreign language. When translating into algebra,
we use we some letter (often x) to represent the
unknown quantity we are trying to determine. It is the
translation process that causes difficulty for some
students. Once the translation is completed, solving is
easy using the techniques we have already reviewed.
Once translate the worlds onto arithmetic expression of
algebraic equations, Example is 1a and 1b and 2a and 2b
are clearly identical. The problem that many students
have is doing the translation. It really isnt very
difficult,
and well show you how.
Look over the following English to algebra dictionary
English words Mathematical
Meaning
Symbol
Is, was, will be, had, has,
will have, is equal to, is
the, same as
Equals =
Plus, more than, sum,
increased by, added to,
exceeds, received got,
older than, further than,
greater than
Addition +
Minus fewer, less than,
difference, decreased by,
subtracted from,
younger than, gave, lost
Subtraction -
Times, of, product,
multiplied by
Multiplication X
Divided by, quotient,
per, for
Division
More than, greater than Inequality >
At least Inequality
Fewer than, less than Inequality
At most Inequality <
What, how, many etc. Unknown
quantity
x (or more
other
variable)
Lets use our dictionary to translate some phrases and
sentences:
1. The sum of 5 and another number is 13; 5 + x = 13
2. John was 2 years younger than Sam; J = S 2
3. Bill has at most $100; B 100
-
4. The product of 2 and a number exceeds that number
by 5; (is 5 more than); 2N = N + 5
In translating statements, you first must decide what
quantity the variable will represent. Often, this is
obvious. Other times there is more than well look at a
few new ones.
INEQUALITIES These problems deal with numbers that are less
than,
greater than, or equal to other numbers. The following
laws apply to all inequalities:
< Means less than, thus 3 < 4
> means greater than, thus 5 > 2
Means less than or equal to, thus 3 4 and 3 3
means greater than or equal to, thus 5 2 and 2 2
Subtracting parts of an inequality from an equation
reverses the order of the inequality.
If x < y, then z x > z y.
If x > y, then z x < z y.
Multiplying or dividing an inequality by a number greater
than zero does not change the order of the inequality.
If x > y, and a > 0, then xa > ya and x/a > y/a.
If x < y, and a > 0, then xa < ya and x/a < y/a.
If 3 < 2 is multiplied through by 2 it becomes 6 > -4
and the order of the inequality is reversed.
Note that negative numbers are always less than
positive numbers. Note also that the greater the
absolute value of a negative number, the smaller it
actually is. Thus, -10 < -9 < -8 < -7, etc.
The product of two numbers with like signs is positive.
If x > 0 and y > 0, then xy > 0
If x < 0 and y < 0, then xy > 0
The product of two numbers with unlike signs is negative
If x < 0 and y > 0, then xy < 0
If x > 0 and y < 0, then xy < 0
Linear inequalities in one unknown. In these problems a
first power variable is given in an inequity and this
variable must be solved for in terms of the inequality.
Examples of linear inequalities in one unknown are: 2x +
7 > 4 + x, 8 y 3 < 2y, etc.
STEP 1: By ordinary algebraic addition and subtraction
(as if it were an equality) get all of the constant terms on
one side of the inequality and all of the variable terms on
other side. In the inequality 2x + 4 < 8x + 16 subtract 4
and 8x from both sides and get -6x 12, dividing by -6 gives x
>2. (The
inequality is reversed). In 3x < 12 dividing by 3 gives x
1/3.
Solve for A in the inequality 10 2a < 0.
Solution: Subtracting 10 from both sides gives -
2a < - 10. Dividing both sides by -2 gives a > -10-
2 or a >5.
Note that the inequality sign has been reversed because
of the division by a negative number,
1. The product of any number of positive numbers
is positive.
For example, 2 3 4 5 = 120 which is positive
or = which is positive.
2. The product of an even number of negative
numbers is positive.
For example, (-3) (-2) = 6 or (-3) (-1) (-9) (-2) = 54
which is positive.
3. The product of an odd of negative numbers is
negative.
For example (-1) (-2) (-3) = -6 or (- ) (-2) (-3) (-6)
(-1) = -18
4. Any number squared or raised to an even power
is always positive or zero.
Evaluation of expressions: To evaluate an expression
means to substitute a value in place of a letter. For
example: Evaluate 3a2-c3; if a = -2, c = -3.
Solution: 3a2-c3 = 3(-2)3 (-3)3 = 3 (4) (-27)
= 12 + 27 = 39
Example: Given a b = ab + b2, Find -2 3 = 3
Solution: Using the definition, we get 2 3 = (-2) (3) +(3)2
= -6 +9 therefore, - 2 3 = 3
-
AVERAGE
The average, or arithmetic mean, of a set of numbers is
the sum of the numbers in the set divided by the total
number of numbers in the set. The formula to remember
is:
=
For example, the average of the numbers 1, 2, 3, 4, 5, 6,
7 is 28 divided by 7 which is 4. The Admission Test
always refers to an average as an average (arithmetic
mean). Just ignore the parenthetical remark so it doesnt
confuse you.
In an averaging problem, you may be asked to find the
total first. For example, suppose a problem states that the
average of 4 test scores is 80 find the sum of the tests.
Recall the formula above. In this case we already know
the average and the number of elements; we need to find
the sum of the tests. Hence, just cross-multiply and the
total of the test scores is the product of the two: 80 4 =
320.
Suppose you are told that two of these scores are 90 and
95 and you want to find the average of the other two
scores. The sum of 90 and 95 is 185. So, the total of the
other two scores is 320-185 = 135. Hence, the average of
the remaining two scores is 135 divided by which is
(67.5).
Do not get confused if two or more of the elements
being averaged are the same. For example, the average
of 5, 5, 5 and 20 is 5+5+5+20 divided by 4 which is 35
divided by 4 which is (8.75). You do not add 5 and 20 and
divide by 2, nor do you add 5 and 20 and divide by 4.
Another situation which may confuse you is when a new
element is added to a set that has already been
averaged. Suppose you take two tests and earn scores of
70 and 80. The average of your two tests is 75. Now,
suppose you take a third test and earn another score 70.
Does your average remain 75? No, your new average is
(70 + 80 + 70)/3 = 73.33. Note that your new average is
NOT (75 + 70) /2 = 72.5. Suppose your third test score
was 75. Then your average over all three tests is still 75
(why?).
Another common error occurs when averaging a set of
numbers that includes 0. For example, what is the average
of 0, 0, 0 and 4? A careless person would say 4, but the
answer is 1! An easy averaging problem can be made
difficult on the Admission Test if certain information is
left out.
Multiple Choice Questions (MCQ)
Fraction: This sub-section will instill a clear
understanding of comparison and approximation of
fractions in you. All that you will need is to take the
approximate value of the fraction to nearest familiar
fraction and then to compare.
1. Of the following, which is greater than ?
a) 4/7 b) 2/5 c) 4/9 d) 1/10
2. Three friends shared a pizza. Tim ate 2/6 of the pizza.
Kate ate 3/6. How much pizza is lef?
a) 0.50 b) c) 1/3 d) 1/6
3. Which of the following fractions is the largest?
a) 3/7 b) 4/9 c) 9/19 d) 11/25
4. The number 0.127 is how much greater than 1/8?
a) 1/500 b) 1/50 c) 2/500 d) 2/50
5. In one classroom exactly one-half the seats are
occupied. In another classroom with double the
seating capacity of the first, exactly three-quarters of
the seats are occupied. If the students from both
rooms are transferred into a third, empty classroom
that has a seating capacity exactly equal to the first
two combined, what fraction of the seats in the third
classroom in occupied?
a) b) 1/3 c) 3/8 d) 2/3 e)
6. Which of the following answer is the sum of the
following numbers: 2 , 2 , 3.3350, 1/8
a) 8.21 b) 9.825 c) 10.825
d) 11.21 e) 12.350
7. In the formula e = h f, if e is doubled and f is halved,
what happens to the value of h?
a) h remains the same. b) h is doubled
c) h is divided by 4 d) h is multiplied by 4
e) h is halved
8. A book dealer received an order in which 1/5 of the
books were hardcover books. The dealer sold 2/3 of
the books, including of the hardcover books. What
fraction of the unsold books were hardcover books?
a) 1/10 b) 3/20 c) 1/5 d) 11/20 e) 4/5
9. A cabdrivers income consists of his salary and tips.
His salary is $50 a week. During one week his tips
were 5/4 of his salary. What fraction of his income
for the week came from tips?
a) 4/9 b) c) 5/9 d) 5/8
10. Eggs cost 90c a dozen. Peppers cost 20c each. An
omelet consists of 3 eggs and of a pepper. How
much will the ingredients for 8 omelets cost?
a) $ 0.90 b) $ 1.3 c) $ 1.80 d) $2.20
11. If each of three grocery stores receives of a
farmers potato crop, a farmers market receives 1/3
of the remaining, and a local fast food restaurant
receives the remaining 200 pounds, how many
pounds of potatoes were in the farmers crop?
-
a) 1400 pounds b) 1200 pounds
c) 900 pounds d) 600 pounds
Finding Value from and Equation
12. If 3x + 4 = 28 + x, the value of x is;
a) 8 b) 12 c) 16 d) 26
13. The solution to the equation x+y = 14, 2x y = - 8 is
a) (7, 7) b) (12, 2)
c) (-2, 12) d) (2, 12)
14. For what values of x is the following equation
satisfied 3x+9 = 21+7x?
a) -3 only b) 3 only
c) 3 or -3 only d) No values
15. If (t2 1) / (t 1) = 2, what value(s) may t have?
a) 1 only b) -1 only c) 1 or 1 d) None
16. If (x-1) (x-2) (x2 4) = , what are the possible value of
x?
a) -2 only b) 2 only c) -1, -2, or -4 only
d) 1, 2 or 4 only e) 1, -2 or 2 only
17. If (t2+2t) / (2t+4) = t/2, what does t equal?
a) -2 only b) 2 only c) any value except 2
d) any value except -2 e) any value
18. One-half of a number is 18 more than one-third of
that number. What is the number?
a) 84 b) 108 c) 102 d) 216
19. If the sum of two numbers is -15 and their product is
56, then these two numbers are roots of which of
the following equations?
a) x2 + 7x +8 b) x2 - 15x +8
c) 2x2 + 7x +8 d) x2 + 15x +56
20. Add one-half percent of 800 to 20% of 200 and
deduct there from 80% of 80. What is the result?
a) 404 b) 408 c) 8 d) None of these
21. A set of 6 flower vases of different sizes cost basket
Tk. 825. Each vase costs 25 Tk. more than the next
on below it in size. What was the cost of the largest
vase?
a) Tk. 175 b) Tk. 185 c) Tk. 200 d) Tk. 215
22. If the sum of five consecutive integers is S, what is
the largest of those integers in terms of S?
a) 10
5 b)
+4
4 c)
+5
4 d)
+10
5
INEQUALITIES
23. If the sum of three consecutive integers is less than
75, what is the greatest possible value of the
smallest one?
a) 22 b) 23 c) 24 d) 25
24. If x < y and a = b, then
a) x + a = y + b b) x + a < y + b c) x + a > y + b
d) x + a = y e) x + a = b
25. If y = 1 + 1/x and x > 1, then y could equal
a) 1/7 b) 5/7 c) 4/7 d) 6/7 e) 8/7
26. The average of all od numbers up to 100 is
a) 51 b) 50 c) 49.5 d) 49
27. The average of 7 Consecutive numbers is 33. The
largest of these numbers is:
a) 36 b) 33 c) 30 d) 28
28. The average of 10 numbers is -10. If the sum of
6 of them is 100, then what is the average of the
other 4 numbers?
a) -100 b) 50 c) -50 d) 100
29. What is the average (arithmetic mean) of all the
multiples of ten from 10 to 190 inclusive?
a) 100 b) 105 c) 90 d) 95
30. The average of 5 quantities is 6. The average of
3 of them is 8. What sit he average of the
remaining two numbers?
a) 4 b) 3.5 c) 3 d) 4.5
31. The average weight of 3 young men is 53kg.
None of them weights less than 51kg. what is the
maximum possible weight of any one man?
a) 53 b) 55 c) 57 d) 59
32. Average of 7 different positive integers is 12.
What is the greatest that any of the integers could
be?
a) 31 b) 47 c) 63 d) 72
33. For a certain student, the average of five test
scores is 83. If four of the scores are 81, 79, 85,
and 90, what is the fifth test score?
a) 84 b) 83 c) 80 d) 79
34. The average age of a group of 12 students is 20
years. If 4 more students join the group, the
average age increases by 1 year. The average age
of the new students is
a) 28 b) 26 c) 24 d) 22
35. After 3 semesters in a college, Jim has a 3.0
GPA. What GPA must Jim attain in his fourth
semester if he wishes to raise GPA to 3.1?
a) 3.5 b) 3.2 c) 3.4 d) 3.3
Answer:
1. A 2. D 3. C 4. A 5. D
6. A 7. D 8. B 9. C 10. D
11. B 12. B 13. D 14. A 15. D
16. E 17. D 18. B 19. D 20. D
21. C 22. D 23. B 24. B 25. E
26. B 27. A 28. C 29. A 30. C
31. C 32. C 33. C 34. C 35. C
Try Some More
1. What values may z have if 2z + 4 is greater than z
6?
a) any value greater than 10
-
b) any value less than -2 c) Any value less than 2
d) any values less than 10 e) None of these
2. In the formula V = r2 h, what is the value of r, in
terms V and h?
a) V/h b) (V/h) c) Vh
d) h/V e) V/(h)
3. In the equation 4.04x + 1.01 = 9.09, what value of x
is necessary to make the equation true?
a) -1.5 b) 0 c) 1 d) 2 e) 2.5
4. What values of x satisfy the equation (x+1) (x+2) = 0.
a) 1 only b) -2 only c) -1 and -2 only
d) 1 and 2 only e) any value between 1 and 2
5. What is the largest possible value of the following
expression: (x+2) (3-x) (2+x)2 (2x 6) (2x + 4)?
a) 576 b) -24 c) 0 d) 12
6. For what value (8) of k is the following equation
satisfied: 2K 9 K = 4K 6 3K?
a) 5 only b) 0 only c) 5/2 only
d) No values e) More than one value
7. In the equation p = aq2 +bq+c, if a = 1, b = -2, and c =
1, which of the following expression p in terms of q?
a) p = (q-2)2 b) p = (q-1)2 c) p = q2
d) p = (q+1)2 e) p = (q+2)2
8. If A+B+C = 10, A + B = 7, and A B = 5, what is the
value of C?
a) 1 b) 2 c) 6 d) 7 e) None
9. If 4m = 9n, what is the value of 7m, in terms of n?
a) 63n/4 b) 9n/28 c) 7n/9
d) 28n/9 e) 7n/4
10. If 2 < a < 5 equals 15, what is the value of 12x
3?
a) a + b must equal 8
b) a + b must be between 2 and 6
c) a+ b must be between 3 and 5
d) a+ b must be between 5 and 8
e) a + b must be between 5 and 11
11. If 6x + 3 equals 5, what is the value of 12x 3?
a) 21 b) 24 c) 28 d) 33 e) 36
12. If 2p + 7 is greater than 3p 5 which of the following
best describes the possible values of p?
a) p must be greater than 2
b) p must be greater than 12
c) p must be less than 2 d) p must be less than 12
e) p must be greater than 2 but less than 12
13. What is the value of q if x2 + qx + 1 = 0, if x = 1?
a) - 2 b) -1 c) 1 d) 2 e) 0
14. What is the value of a2+4ab2+4b3, if a = 15, b = 5?
a) 1625 b) 2125 c) 2425
d) 2725 e) 2225
15. If A+ b = 12, and B + C = 16, what is the value of A-C?
a) -4 b) -28 c) 4 e) 28
16. For what value of x does x2 + 3x + 2 = 0
a) -1 only b) 2 only c) 1 or -2 only
d) 1 or 2 only c) none of these
17. If a + b equals 12, and a b equals 6. What is the
value of b?
a) 0 b) 3 c) 6 d) 9
18. If x = 0, and y = 2, and x2yz + 3xz2 + y2z + 3y + 4x =
0,
what is the value of z?
a) 4/3 b) 3 /2 c) 3/4 d) 4/3
19. If 3 > x > 7, and 6 > x > 2, which of the
following best
describes x?
a) 2 < X < 6 b) 2 < X < 7
c) 3 < X < 6 d) 3 < X < 7
20. If x + y = 4, and x + z= 9, what is the value of (y-z)?
a) 5 b) 5 c) 13 d) 13
21. If +5
15=
5
3, then m =
a) 4 b) 8 c) 10 d) 12 e) 20
22. If 2+4+6
2+3+7= 1, then x = ?
a) 0 b) -1 c) 7/6 d) 6 e) 1
23. The sum of , 1/3, 1/8, 1/15 and 1/5 is:
a) 41/40 b) 16/15 c) 6/9
d) 49/40 e) none
24. Which of the following is true?
a) 0 < 1/10 < .01 b) 0.12 < 1/8 < 0.13
c) 0.3 < < 0.5 d) 0.3 < 1/3 < 0.33
25. Which of the following fraction is the largest?
a) 12/15 b) 5/6 c) 17/21 d) 11/14
26. Which of the following is greater than I?
a) 0.00004
.005 b)
0.000006
.0001
c) 0.01
.003 d)
0.0003
.0006
27. There are 30 students enrolled in a Business School.
Of the enrolled students, 9/10th took the final exam.
1/3rd of the students who took the final exam passed
it. How many students passed the final exam?
a) 3 b) 4 c) 5 d) 9
28. What number must be added to the numerator and
denominator of to give 11/12?
a) 5 b) 6 c) 7 d) 8
29. 2
100+
7
10000+
4
5000=?
a) 0.0278 b) 0.02078 c) 0.020078 d) None
30. If two places are one inch apart on a map, then they
are actually 160 miles apart. (The scale one the map
is one inch equals 160 miles). If section is 27
8 inches
from Monroe on the map, how many miles is it from
section to Monroe?
a) 3 b) 27 c) 300 d) 460
31. Three sixteenths of a pole measures 54 inches in
length. Then what is the length of the pole in feet?
a) 10 b) 20 c) 24 d) 30
32. A business is owned by 9 women and 1 man, each of
whom owns an equal share. If one of the women
sells of her share to the man, and another woman
-
keeps 1/5 of her share and sells the rest to the man,
what fraction of the business will the man own?
a) b) 11/32 c) 23/100 d) 7/8
33. Which of the following fraction is the largest?
a) 2/3 b) 3/5 c) 7/11 d) 13/23
34. Which of the following fractions is the smallest? a) 5/6 b)
12/15 c) 11/14 d) 29/35
35. Five times a number less 3 is 32. What is twice the
number?
a) 5 b) 7 c) 16 d) None of these
36. The difference between the sum of two numbers
and the difference of the two numbers of 6. Find the
larger of the two numbers if their product is 15.
a) 3 b) 5 c) 17 d) 20
37. If 4x is 6 less than 4y, then y x =?
a) -24 b) 24 c) -3/2 d) 3/2
38. If x is a positive number and x2 + 4 = 125, what is the
value of x?
a) 10 b) 11 c) 12 d) 13
39. What is the largest value of x that satisfies the
equation 2x2 3x = 0?
a) 0 b) 1 c) 1.5 d) 2
40. If x = 3 and y = 1/6, then the value of x in terms of y is
-
a) 8y b) 25y c) 12y d) 18y
41. Last year, Allis and jack together won 40 tennis
matches. Allis won 8 more matches than Jack. How
matches did Allis win?
a) 19 b) 16 c) 24 d) 22
42. Sum of the two numbers of 23 and the difference is
21. Find out the smaller one of the two numbers.
a) 2 b) 4 c) 1 d) 3
43. If p 1 / p = 5, find the value of (p + 1/p)2
a) 24 b) 19 c) 29 d) 30
44. If x + 1 < 3x + 5, then
a) x < - 2 b) x > - 2 c) x = - 2 d) x < 2
45. The average of 4 numbers is X. If the average of
first 3 numbers is Z, what is the third number?
a) 4X Y Z b) 3Y 2Z
c) 3Y + 2Z + 4X d) 4X Y Z
46. If is the first of five consecutive odd numbers,
what is their average?
a) b) + 1 c) + 2
d) + 3 e) + 4
47. The average age of a committee of 8 members is
40 years. A member aged 55 years retired and
another member aged 39 years took his place.
The average age of the present committee is
a) 29 years b) 38 years
c) 21 years d) None
48. What is the average of the following numbers
3.2, 47/12, 10/3?
a) 3.55 b) 10/3 c) 103/30
d) 209/60 e) 1254/120
49. Ashraful bowled 4 games and scored an average
of 30 points. What score could he receive on his
fifth game if he wants to have an overall average
that is a multiple of 7, his favorite number?
a) 20 b) 15 c) 21 d) 35
50. The average age of a family of 6 matches is 22
years. If the age of the youngest member be 7
years, the average age of the family at the birth
of the youngest member was:
a) 15 years b) 17 years
c) 18 years d) 19 years
51. During a 10 day period, Saikat received the
following number of phone calls each day: 2, 3,
9, 3, 5, 7, 7, 10, 7, 6. What is the average
(arithmetic mean) of the median and mode of this
set of data?
a) 7.00 b) 6.50 c) 6.75 d) 7.50
52. The average weight of five persons of a group
was 160 lbs. A person left the group whose
weight is 150 lbs. and a new person join the
group. As a result, the average weight became
155 lbs. what is the weight of the new person?
a) 120 b) 125 c) 135 d) 145
53. In cricket team, the average age of 11 players is
28 years. Out of these the averages ages of three
groups of three players each are 25 years, 28
years, and 30 years respectively. If in these
groups, the captain is 11 years older than the
youngest player, what is the age of the captain?
a) 33 years b) 34 years
c) 35 years d) 36 years
Answer:
1. A 2. E 3. D 4. C 5. C 6. D 7. B
8. E 9. A 10. E 11. A 12. D 13. A 14. E
15. A 16. C 17. B 18. B 19. B 20. A 21. E
22. E 23. D 24. C 25. B 26. C 27. D 28. D
29. B 30. D 31. C 32. C 33. A 34. C 35. D
36. B 37. D 38. B 39. C 40. D 41. C 42. C
43. C 44. B 45. B 46. E 47. B 48. D 49. A
50. C 51. C 52. B 53. C
