Question 1

Which of the following is not a prime number?1, 7, 11, 13
A)1
B)7
C)11
D)13

Accepted Answer

A prime number is a number which is exactly divisible only by itself and 1. Example: 7, 11, 13 etc. Number 7 is not exactly divisible by any number other than 1 and 7. One (1) is not a prime number. The number 1 has only one factor and is not considered to be a prime number
Key takeaway: A prime number is a number which is exactly divisible by itself and 1 only. It is not exactly divisible by any other number. In GMAT questions based on prime numbers are commonly asked. It is useful to remember the first 15 Prime numbers 2,3,5,7,11,13,17,19,23,29,31,37,41, 43 and 47.

Question 2

Find median of 21, 3, 9, 6, 56, 24, and 4
A)16
B)7)5
C)17.5
D)9

Accepted Answer

`Median is the value of the number in the middle position of a list of numbers arranged in increasing (or decreasing) order. The series after arrangement is 3, 4, 6, 9, 21, 24, and 56. The 3rd term is in the middle and its value is 9.
Key takeaway: Mean, median and mode are measures of central tendency of data. It is easy to find median. However the series must be arranged in an ascending or descending order before finding the median.

Question 3

The sum of first four prime numbers is
A)10
B)11
C)16
D)17

Accepted Answer

A prime number is a natural number larger than 1 which does not have divisors other than itself and one. The first four 2, 3, 5 and 7. The sum=17
Key takeaway: 0 and 1 are not prime numbers. 2,3,5,7,11,13,17,19,23,… are prime numbers. You can check none of these numbers can be divided by any number other then themselves or 1.

Question 4

A rectangular field ABCD has a flower garden which is 18 feet by 6 feet. If the garden covers 30 percent of the field, what is the area, in square feet, of the field?
A)130
B)216
C)360
D)540

Accepted Answer

The area of the garden is equal to 18X6=108, garden is 30% of the field. As 30% is equal to 108, 100% is equal to 108/30X100=360.
Key takeaway: Area of rectangle is equal to length X width. Questions based on area of standard geometrical figures such as rectangle, square, triangle, circle, etc are asked. List out their formulae and practice over them.

Question 5

(1+?3)(1-?3)=
A)-3
B)-2
C)4
D)3-2?3

Accepted Answer

a²-b²=(a+b)X(a-b). So the given value is equal to 1²-(?3)²=-2 Key takeaway: The square root of the numbers like ?3 is a decimal number and expression would require long calculation if we put in the given. So look for a way to attack such problems other way than straight arithmetic calculation. You should be able to find application of simple algebraic formulae.

Question 6

If diagonal of a square room is x, what is the area of the room? A)x/2 B)x/?2 C)2x D)x²/2

Accepted Answer

A square is a rectangle whose all sides are equal. Its area is equal to square of its sides. Area= (side)² Diagonal x²=2(side)², Area=x²/2. Key takeaway: The word problems based on basic geometry are easy to tackle if you remember simple formulae (perimeter, area) of rectangle, square, circle etc. and their applications. Practice over relationships of length, width perimeter and area rectangle and square.

Question 7

If the length and width of a rectangular garden plot were each increased by 10 percent, what would be the percent increase in the area of the plot?
A)20
B)21
C)12
D)11

Accepted Answer

If length l is increased by 10%, it becomes 1.1 l. Similarly width becomes 1.1 w. Area = length X width = 1.1 l X 1.1 w = 1.21lw. Thus, the area lw increases to 1.21lw. Hence the increase is 21%.
Key takeaway: While multiplying decimal number, be careful in placing decimal at proper place.

Question 8

Rectangular floors X and Y have equal area. If floor X is 8 feet by 27 feet and floor Y is 9 feet wide, what is the length of floor y, in feet?
A)24
B)21
C)18
D)20

Accepted Answer

Area of rectangle = length X width, 8X27=9Xw, w= (8X27)/9=24
Key takeaway: Area of rectangle is equal to the product of its length and width. Compare two geometrical figures to find out missing information.

Question 9

A rectangular carton in 10 cm long, 15 cm wide and 5 cm high. If, the length, the width and the height each is doubled, what will be its volume, in cubic cm?
A)20
B)60
C)1500
D)6000

Accepted Answer

Volume V= length x width x height = l x w x h = 10x15x5= 750. The length, the width and the height each is doubled. Hence, Volume of new carton = 2 l x 2 w x 2h = 8 V = 8 x 750 = 6000 square cm.
Key takeaway: Sometimes, the actual arithmetical calculations are not required. You can apply logic and save time.

Question 10

Which of the following is equal to x20 for all positive values of x? A)(x¹⁰ + x¹⁰ ) B)(x²)¹⁰ C)(x²)¹⁰. D)(x⁵)¹⁵

Accepted Answer

It is raising exponents with same base. Here powers are multiplied (2X10 =20). (X²)¹⁰= X ^(2x10) = X²⁰ Key takeaway: It is easy to simplify any exponent question if you remember following formulae: a^m x aⁿ = a^m+n, a^m / aⁿ = a^m-n , (am ) ⁿ = a^{m x n} , (a^m )^1/n = a^{m/ n}

Question 11

A card is picked up at random from a pack of 52 cards. Find the probability that it is a king or queen.
A)2/13
B)3/13
C)7/52
D)1/13

Accepted Answer

In a pack of 52 cards, there are 8 cards which is either king or queen. A card is picked up at random from a pack of 52 cards. The probability that it is a king or queen = 8/52 = 2/13
Key takeaway: Probability means the chance of occurrence of an event. It is an important mathematical concept that we use in our day-to-day life. Practice some simple problems to understand the concept.

Question 12

A box contains tickets numbered 01 to 100. What is the probability that a ticket selected at random will have number with a tenth digit of 5?
A)1/5
B)9/10
C)1/10
D)½

Accepted Answer

The tenth digit of 5 is 05, 15, 25 ....., and 95. i.e. 10 possible numbers out of 100 numbers.
Probability P = favourable events for success / total possible events = 10/100 = 1/10.
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.

Question 13

A series discount of 20% and 10% is equivalent to a single discount of
A)30%
B)28%
C)22%
D)27%

Accepted Answer

Let original price=100, Sale price after 1st discount = 100 -20 =80. Second discount = 10% of 80 = 8, Net price = 72. Total discount on original price of 100 = 28. A series discount of 20% and 10% is equivalent to a single discount of 28%
Key takeaway: First discount is given on the original sale price, but second discount is on already discounted price and not on the original sale price.

Question 14

The product of two numbers is 1600 and their Highest Common Factor ( H.C.F.) is 5. The Lowest Common Multiple (L.C.M.) of the numbers is _______
A)320
B)1595
C)1605
D)8000

Accepted Answer

The product of two numbers is equal to their Highest Common Factor ( H.C.F.) and Lowest Common Multiple (LCM). LCM = 1600/ 5 = 320
Key takeaway: This is a fundamental rule and you can solve the questions in a simple way.

Question 15

At simple interest, a sum doubles in 20 years. The rate of interest per annum is ____
A)5%
B)10%
C)12%
D)20%

Accepted Answer

Simple Interest I = P x R x T . Sum doubles in 20 years. So interest I = P;
P=PxRxT R =1/T = (1/20 ) % = 5%
Key takeaway: Simple Interest is charged only on the original principal, not on the interest accrued. In compound interest, interest is given on interest also besides on the principle amount.

Question 16

If Set A is a set of first 5 odd numbers and Set B is a set of first 5 prime numbers. Find Set A?B.
A){1,3,5,7,9}
B){1,3,5,7,9,11}
C){2,9,11}
D){3,5,7}

Accepted Answer

A?B is the intersection of sets A and B and is defined as the set that have all the elements which are common in both sets. Set A (1,3,5,7,9) B= (2,3,5,7,11) Numbers 3, 5 and 7 are common.
Key takeaway: Set theory is important for GMAT. Simple questions based on the understanding of basic rules of set theory are asked. Learn these rules.

Question 17

Find the sum of all angles of a regular hexagon.
A)720
B)360
C)540
D)180

Accepted Answer

The sum of all (interior) angles of a polygon is given by the formula (2n-4) X90 where n is the number of sides. Hexagon is a polygon with 6 sides. Hence sum is = 720.
Key takeaway: Direct questions based polygons are asked. You should familiarized basic formulae and visualization of various shapes of two dimensional figures.

Question 18

A sum of money at simple interest amounts to N2240 in 2 years and N 2600 in 5 years. The sum is:
A)1880
B)2000
C)2120
D)2360

Accepted Answer

Area of trapezium = 1/2 (sum of length of parallel sides) X height 42 = 1/2 (6+8) X h. H=6 cm.
Key takeaway: A trapezium is a quadrilateral with only two sides parallel to each other. In some cases you may have to calculate height.

Question 19

Find the value of log3 (9X27X81)
A)3
B)9
C)27
D)81

Accepted Answer

The logarithm of a product is equal to the sum of the logarithms of the individual number. The logarithm of a number, the number being same as the base is 1. log3 (9X27X81) = log3 9 + log3 27 + log3 81 = 2 log3 3+ 3 log3 3 +4 log3 3 = 2 + 3 + 4 = 9
Key takeaway: While learning logarithm pay more attention to the basic rules of logarithm and develop an understanding of the range of the values of logs.

Question 20

Three drums contain 12 litres, 15 litres and 24 litres of milk. What can be the size of biggest measuring pot to measure all the quantities exactly?
A)3
B)24
C)12
D)120

Accepted Answer

The Greatest Common Divisor (GCD) is the largest positive integer that divides all the given numbers. Hence the GCD is the biggest size of measuring pot. So find GCD of 12, 15 and 24.
12= 2x2x3
15= 3x5
24= 2x2x2x3
3 is Greatest Common Divisor and so the size of biggest measuring pot to measure all the quantities 12 liters, 15 liters and 24 liters exactly is 3 liters.
Key takeaway: GCF is also known as the Highest Common Factor (HCF) or the Greatest Common Factor (GCF).It is the largest positive integer that divides all the given numbers. Write each number as products of their prime factors. Write out all prime factors that are common to all the numbers. Their product is the GCF.

Quiz 2: (ICE): Mathematics: Part a

Which of the following is not a prime number?1, 7, 11, 13

Find median of 21, 3, 9, 6, 56, 24, and 4

The sum of first four prime numbers is

A rectangular field ABCD has a flower garden which is 18 feet by 6 feet. If the garden covers 30 percent of the field, what is the area, in square feet, of the field?

(1+?3) (1-?3) =

If diagonal of a square room is x, what is the area of the room?

If the length and width of a rectangular garden plot were each increased by 10 percent, what would be the percent increase in the area of the plot?

Rectangular floors X and Y have equal area. If floor X is 8 feet by 27 feet and floor Y is 9 feet wide, what is the length of floor y, in feet?

A rectangular carton in 10 cm long, 15 cm wide and 5 cm high. If, the length, the width and the height each is doubled, what will be its volume, in cubic cm?

Which of the following is equal to x20 for all positive values of x?

A card is picked up at random from a pack of 52 cards. Find the probability that it is a king or queen.

A box contains tickets numbered 01 to 100. What is the probability that a ticket selected at random will have number with a tenth digit of 5?

A series discount of 20% and 10% is equivalent to a single discount of

The product of two numbers is 1600 and their Highest Common Factor ( H.C.F.) is 5. The Lowest Common Multiple (L.C.M.) of the numbers is _______

At simple interest, a sum doubles in 20 years. The rate of interest per annum is ____

If Set A is a set of first 5 odd numbers and Set B is a set of first 5 prime numbers. Find Set A?B.

Find the sum of all angles of a regular hexagon.

A sum of money at simple interest amounts to N2240 in 2 years and N 2600 in 5 years. The sum is:

Find the value of log3 (9X27X81)

Three drums contain 12 litres, 15 litres and 24 litres of milk. What can be the size of biggest measuring pot to measure all the quantities exactly?