Question 1

If 36 is 30 percent of 30 percent of a certain number, what is the number?
A)9
B)36
C)81
D)400

Accepted Answer

Assume the original number is 100. Its 30% is 30. Again 30% of 30 are 9. Thus 9 are 30 percent of 30 percent of 100. Hence 36 are 30 percent of 30 percent of 400.
Key takeaway: In such percent problem, do not add percents. For example 30% of 30% is not 60%. It is 9%.

Question 2

If x= (0.05)2, y=1/ (0.05)2, and z= (1-0.05)2-1, which of the following is true?
A)X=y=z
B)Y<z<x
C)Z<x<y
D)Y< and x=z

Accepted Answer

First simplify and express x ,y and z in decimal and then compare
x = 0.0025, y = 400 z = -0.0975
z <x<y
Key takeaway: While comparing decimal numbers or negative numbers, be careful and try to visualise mentally their position on the line number. Negative numbers are less than the positive numbers. And 0.09 is less than 0.01

Question 3

What is the value of (0.2)5 ?
A) 0.00032
B) 0.0016
C) 0.008
D )0.32

Accepted Answer

Tackle the problem in two stages. First find the value of exponent ignoring the decimal. Second, find the position of the decimal.
2² = 2 x2 x 2 x2 x 2 x 2 = 32
(0.2)? = 0.2 x 0.2 x 0.2 x 0.2 x 0.2 x 0.2 = 0.00032
Key takeaway: In decimal based exponents' problems, be careful in placing decimal at correct position.

Question 4

What is the maximum number of 2 ½ foot pieces of wire that can be cut from a wire that is 48 feet long?
A)11
B)18
C)19
D)20

Accepted Answer

48 divided by 2 ½ = 48 divided by 5/2 = 48÷5/2 = 48 x 2/5 = 19.2
19 pieces of 2 ½ foot each. The 20th piece will be of smaller size.
Key takeaway: Division by 10 is easy. So if you have to divide by 2 ½, first divide the number by 10 and then multiply by 4

Question 5

If the number 1/6, 2/9, 1/18, 1/12, and 2/3 were ordered from greatest to least, the middle number of the resulting sequence would be
A)1/6
B)2/9
C)1/18
D)1/12

Accepted Answer

Before comparing fractions, their denominators should be made same. The denominators 6, 9, 18, 12 and 3 have LCM = 36. We convert the fractions all with 36 as denominator.
6/36, 8/36, 2/36, 3/36, 24/36
Now arrange the series from greatest to lowest value of their numerators:
24/36, 8/36, 6/36, 3/36, 2/36
The middle number of the resulting sequence is 6/36 = 1/6
Key takeaway: Before comparing fractions, their denominators should be made same. Then arrange the series in ascending order as per the numerators.

Question 6

{(6) (0.144)}/2.16 =
A) 0.04
B) 0.3
C) 0.4
D) 4.0

Accepted Answer

In given problem, denominator 2.16 = 6 x 0.36 and you can cross 6. The expression reduces to 0.144/0.36 = 0.4 x 0.36/0.36 =0.4
Key takeaway: While simplifying and reducing fraction, visualise mentally to find whether the any term in the numerator and the denominator has common factors. Then cancel or cross out common factors.

Question 7

Divide $680 among A, B and C such that A gets 2/3 of what B gets and B gets 1/4th of what C gets . Now the share of C is?
A)300
B)360
C)420
D)480
E)500

Accepted Answer

Assume C gets z.
B gets 1/4 z
and A gets 2/3 of B = 2/3 X 1/4 z = 1/6 z
z + ¼ z + 1/6 z = $680
(24z +6z +4z)/24 = $680
z = 480
Key takeaway: The GMAT often contains problems in which you are given ratios or proportional , from which one piece of information is missing. It is important to understand the logic of the word problem correctly before cracking it

Question 8

If (-7) (3/x+9)=0 and x?7, then x=
A)-27
B)-3
C)-1/3
D)1/3
E)3

Accepted Answer

The equation has two factors on its left hand , one of these must be equal to zero .
As -7 is not zero , hence (3/x+9)=0 or 3/x = -9 or x = -3/9 = -1/3

Question 9

Find the probability of getting 2 Heads when two fair coins are tossed?
A)1
B)2/3
C)½
D)¼
E)¾

Accepted Answer

A coin has two faces Head(H) and Tale(T). The possible outcome when two coins are tossed is HH, TT, HT and TH. Out of 4 possible outcomes only 1 is favourable for getting both Heads. Probability is the ratio of favorable events for success and total possible events. Hence Probability P = 1/4
Key takeaway: Probability is the chance of the occurrence of an event . It is the ratio of favourable events for success and total possible events. It is an important mathematical concept that we use in our day-to-day life. Practice some simple problems to understand the concept.

Question 10

A series of discount of 10%, 20% and 40% is equal to a single discount of
A)50%
B)56.8%
C)70%
D)70.28%
E)80%

Accepted Answer

Assume original price = 100
Sale price after first discount of 10% = 100- 10% = 90
The second discount is given on the net sale price after first discount.
Sale price after second discount of 20% = 90- 20% = 72
Sale price after first discount of 40% = 72- 40% = 72-28.8 =43.2
Total discount on 100 =100- 43.2 = 56.8 = 56.8%
Key takeaway: The discount is given on the sale price. If there are series of discounts, the discount is worked out on previously discounted price and not on original sale price.

Question 11

Which of the following is greater than 1/3?
A)33/100
B)4/11
C)3/10
D)13/54
E)5/16

Accepted Answer

You can change numerator of 1/3 by multiplying both numerator and denominator by the same numbers.
1/3 = 33/99 , 4/12, 3/9 and 5/15
33/100 <33/99
4/11 >4/12
3/10 < 3/9
5/16 <5/15
4/11 is greater than 1/3
Key takeaway: The GMAT often asks you to compare two or more fraction and decide which is larger. Use the Bowtie technique to find the common denominator. This technique is also used to add or subtract. Compare the first two fractions and eliminate the smaller one and then compare with next fraction; and so on.

Question 12

Three machines, individually, can do a certain job in 2, 3 and 4 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?
A)13/12
B)¾
C)5/6
D)6/5

Accepted Answer

The greatest part of the job that can be done in one hour by the two fastest of the three machines i.e. by first two machines.
In 1 hr the first machine does ½ work and the second machine does 1/3 work.
So in hour both machines working together do ½ + 1/3 = 5/6 works
Key takeaway: In the questions based on time and work, take the total work to be done as one unit of work. Remember the basic concept that if A does a work in x hour , the in one hour A does 1/x of the work in 1 hour.

Question 13

One side of a rectangular field is 4 meters and its diagonal is 5 meters. The area of the field is:
A)12 m2
B)15 m2
C)20 m2
D)4?5 m2

Accepted Answer

First find the other side of the rectangle . L2 +B2 = D2
B2 = D2 - L2 = 25-16 =9
B= 3 meter
Area = L x B = 4 X 3 = 12 m2
Key takeaway: In GMAT, word problems based on only basic geometry are asked . You should remember simple formulae ( perimeter, area ) of rectangle, square, circle etc. and their application.

Question 14

In an examination of 4 subjects, John gets 100, 60 and 55 in three subjects. If his average (arithmetic mean) marks for all four subjects is 75, then the marks in the 4th subject must be
A)82
B)85
C)88
D)91
E)93

Accepted Answer

The average marks for all four subjects is 75 and so total marks are 4 x 75 = 300
The marks for three subjects are given and their total is 100 +60 + 55 = 215. Hence the marks for the fourth subject = 300- 215 = 85
Key takeaway: GMAT always refers to an average as average (arithmetic mean) The average ( arithmetic mean ) of a set of numbers is their sum divded by the number of numbers in the set. For average problems, think Total divided by number of items.

Question 15

$\sqrt(25+25 )$ =
A)5$\sqrt2$
B)10$\sqrt2$
C)25$\sqrt2$
D)10
E)25

Accepted Answer

Do not add 25 and 25. Think how to take some figures out of square root symbol. You notice 25 can be taken common
$\sqrt(25+25 )$ =$\sqrt(25)(1+1 ) $= 5$\sqrt(1+1 )$ = 5$\sqrt2$
Key takeaway: You are not expected to know the square root of the numbers like 50 So look for a way to attack such problems other way than straight arithmetic calculation. You should be able to find some factors or application of simple algebraic formulae.

Question 16

What is the ratio of 4/5 to the product 5(4/5)?
A)1/5
B)5/16
C)16/5
D)5

Accepted Answer

Put the two terms as fraction and cross common factors
(4/5)/ 5 (4/5) = 1/5
Key takeaway: The ratio of two terms can be expressed as a fraction Look for some common factors both in the numerator and the denominator and cancel them. It generally does not require arithmetic calculations.

Question 17

If 3x-5= 15-x, then 3x=
A)-15
B)5
C)15
D)25

Accepted Answer

This is a simple algebraic equation with one variable x. Try to bring all terms with x on one side and all other terms on the other side of the equation.
3x -5 = 15 - x
3x + x = 15 +5
4x= 20 or x = 5
But the question asks for value of 3x which is 15 and not 5.
Key takeaway: To solve simple equations, use mathematical operations such as add, multiply to isolate the variable . Get the variable alone on one side of the equal sign

Question 18

What number when multiplied by 6/11 yields 9/11 as the result?
A)3/11
B)2/3
C)3/2
D)11/3

Accepted Answer

If you divide the product of the two numbers by one number you get another number.
(9/11) / (6/11) = 9 x 11 / 6 x 11 = 9/6 = 3/2
Key takeaway: In fractions, always look for some common factors both in the numerator and the denominator and cancel them. It generally requires simple arithmetic calculations only.

Question 19

If (x+6) is a factor of x2+mx-48, then m=
A)16
B)12
C)2
D)6
E)14

Accepted Answer

This is a quadratic equation. Use the formula if and b are solutions of a quadratic equation then it can be expressed as x2 + (a-b) x - ab = 0
or (x+a) (x-b) = 0
Given x+6 is a factor So a= 6
(a-b) = m and ab =-48
Hence b = 8 and m =2
Key takeaway: The general form of a quadratic equation is x2 + (a+b) x + ab = 0 and can be expressed as product of two terms (x+a)(x+b) = 0, a and b are called two roots or solutions of the equation The values x =a or b satisfy the equation.

Question 20

62/250=
A) 0.248
B) 0.252
C) 0.284
D) 0.312
E) 0.320

Accepted Answer

Look at the denominator and think how to covert it in 1000 .If multiply both numerator and denominator by 4, you get 62 x 4/1000 = 248/1000 = 0.248
Key takeaway: One way may be to go for straight arithmetic calculation But the question may require long calculation It may waste time and also chances of committing error would be more . So always first look for a way to attack such problems other way such as multiplying or dividing both numerator and denominator by a common number.

Quiz 5: Math: Mathematics Advanced

If 36 is 30 percent of 30 percent of a certain number, what is the number?

If x= (0.05) 2, y=1/ (0.05) 2, and z= (1-0.05) 2-1, which of the following is true?

What is the value of (0.2) 5 ?

What is the maximum number of 2 ½ foot pieces of wire that can be cut from a wire that is 48 feet long?

If the number 1/6, 2/9, 1/18, 1/12, and 2/3 were ordered from greatest to least, the middle number of the resulting sequence would be

{(6) (0.144) }/2.16 =

Divide $680 among A, B and C such that A gets 2/3 of what B gets and B gets 1/4th of what C gets . Now the share of C is?

If (-7) (3/x+9) =0 and x?7, then x=

Find the probability of getting 2 Heads when two fair coins are tossed?

A series of discount of 10%, 20% and 40% is equal to a single discount of

Which of the following is greater than 1/3?

Three machines, individually, can do a certain job in 2, 3 and 4 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working together at their respective rates?

One side of a rectangular field is 4 meters and its diagonal is 5 meters. The area of the field is:

In an examination of 4 subjects, John gets 100, 60 and 55 in three subjects. If his average (arithmetic mean) marks for all four subjects is 75, then the marks in the 4th subject must be

$\sqrt(25+25 )$ =

What is the ratio of 4/5 to the product 5(4/5) ?

If 3x-5= 15-x, then 3x=

What number when multiplied by 6/11 yields 9/11 as the result?

If (x+6) is a factor of x2+mx-48, then m=

62/250=