GMAT Quant Question Bank

In Milton school, the number of students who play Badminton is thrice the number of students who play Tennis. The number of students who play both the sports is thrice the number of students who play only Tennis. If 60 students play both the sports, how many students play only Badminton? (incorrect) (A) 100 (B) 150 (C) 160 (D) 180 (E) 120

60 = 3 (x − 60) => x = 80 Thus, the number of students play only Badminton = 3x − 60 = 180 The correct answer is Option C.

In a batch of dresses, 1/4 of the dresses are traditional and 3/4 of the dresses are contemporary. Half the dresses are for males and half are for females. If 100 out of a lot of 1,000 dresses are traditional and for males, how many of the dresses are contemporary and for females? (A) 150 (B) 250 (C) 300 (D) 350 (E) 400

8. Total number of dresses = 1,000 Number of traditional dresses = 250 Number of contemporary dresses = 750 Number of dresses for males = Number of dresses for females = 100/2 = 500 Number of traditional dresses for males = 100

Incorrect: In a survey of 320 employees, 35 percent said that they take tea, and 45 percent said that they take coffee. What percent of those surveyed said that they take neither tea nor coffee? (1) 25 percent of the employees said that they take coffee but not tea. (2) 400/7 percent of the employees who said that they take tea also said that they also take coffee

= (100 − 60)% = 40% - Sufficient From statement 2: Percent of employees who take tea = 35%. Thus, percent of employees who tea as well as coffee (x%) = 400 7 % of 35% = 4 7 × 35% = 20% This is the same information as obtained from statement 1. - Sufficient The correct answer is Option D.

. In a conference, if each of the 1,230 participants ordered for either Tea or Coffee (but not both), what percent of the female participants ordered for Coffee? (1) 70 percent of the female participants ordered Tea. (2) 80 percent of the male participants ordered Coffee

From statement 1: It is known that each of the participants ordered for exactly one drink. We also know that 70 percent of the female participants ordered Tea. Thus, the remaining (100 − 70)% = 30% of the female participants ordered Coffee. - Sufficient From statement 2: There is no information about the female participants. - Insufficient The correct answer is Option A.

If each of the 10 students working with an NGO received cash prize, was the amount of each cash prize the same? ] (1) The standard deviation of the amounts of the cash prizes was 0. (2) The sum of the 10 cash prizes was $500

From statement 1: Standard deviation (SD) is a measure of deviation of items in a set with respect to their arithmetic mean (average). Closer are the items to the mean value, lesser is the value of SD, and vice versa. Thus, it follows that if a set has all equal items, its SD = 0. Since the SD of the amounts of the 10 prizes is '0', the amount for each prize must be same. - Sufficient From statement 2: The total amount of the 10 prizes will not help us to determine whether the amount for each prize was the same. - Insufficient The correct answer is Option A

A marketing class of a college has a total strength of 30. It formed three groups: G1, G2, and G3, which have 10, 10, and 6 students, respectively. If no student of G1 is in either of the other two groups, what is the greatest possible number of students who are in none of the groups? (A) 4 (B) 7 (C) 8 (D) 10 (E) 14

Number of students on the committee G1 = 10. As no member of G1 is in either of the other two groups, the above 10 students belong to only G1. However, there may be an overlap with the students of G2 and G3. Number of students in G2 = 10. Number of students in G3 = 6. We would get the greatest number of students who would not be in any of the groups if there is maximum overlap between the students of G2 and G3. The maximum overlap between the students of G2 and G3 would be the minimum of the number of students in the two groups i.e. minimum of 6 and 10 = 6. Thus, we have G2 ∩ G3 = 6 Thus, the number of students in G2 or G3 = G2 + G3 − G2 ∩ G3 = 10 + 6 − 6 = 10 Thus, total number of students belonging to one of more groups = G1 + G2 or G3 = 10 + 10 = 20.

Principal of a school recorded the number of students in each of the 15 classes. What was the standard deviation of the numbers of students in the 15 classes? (1) The average (arithmetic mean) number of students for all the 15 classes was 30. (2) Each classes had the same number of students.

Standard deviation (SD) is a measure of deviation of items in a set w.r.t. their arithmetic mean (average). Closer are the items to the mean value, lesser is the value of SD, and vice versa; thus, it follows that if a set has all equal items, its SD = 0. From statement 1: Statement 1 is clearly insufficient as we do not know how many numbers of students are there in each class; merely knowing the mean value is insufficient. From statement 2: Statement 2 is clearly sufficient. As discussed above since each class has an equal number of students, their mean = number of students in each class, so SD = 0: no deviation at all! The correct answer is Option B

Is the standard deviation of the scores of Class A's students greater than the standard deviation of the scores of Class B's students? (1) The average (arithmetic mean) score of Class A's students is greater than the average score of Class B's students. (2) The median score of Class A's students is greater than the median score of Class B's students.

Standard deviation (SD) is a measure of deviation of items in a set with respect to their arithmetic mean (average). Closer are the items to the mean value, lesser is the value of SD, and vice versa; this follows that if a set has all equal items, its SD = 0. From statement 1: We know that the average score of Class A's students is greater than the average score of Class B's students. However, we have no information about the deviations of the scores of the students about the mean. Hence, we cannot compare the standard deviations. - Insufficient From statement 2: We know that the median score of Class A's students is greater than the median score of Class B's students. However, we have no information about the deviations of the scores of the students about the mean. Hence, we cannot compare the standard deviations. - Insufficient Thus, from statements 1 and 2 together: Even after combining the two statements we cannot determine the deviation of the scores of the students about the mean. - Insufficient The correct answer is Option E

An equilateral triangle that has an area of 8√ 3 is inscribed in a circle. What is the area of the circle? (A) 4π (B) 8π/3 (C) 32π/3 (D) 6 √ 3 π (E) 10√ 3 π

Thus, the centre of the circle (O) is the centroid of the equilateral triangle ABC. T he centroid divides the median AD in the ratio 2 : 1. Thus, we have AO = 2/ 2 + 1 × AD = 2/3 × 2 √ 6 = 4 √ 6/3 Thus, the radius (r) of the circle = AO = 4 √ 6/3 Thus, the area of the circle = πr 2 = π × (4 √ 6/3 ) ^ 2 = 32π 3 The correct answer is Option C.

A company has a total of x employees such that no two employees have the same annual salary. The annual salaries of the x employees are listed in increasing order, and the 22nd salary in the list is the median of their annual salaries. If the sum of the annual salaries of all the employees is $860,000, what is the average (arithmetic mean) of the annual salaries of all the employees? (A) $19,500 (B) $20,000 (C) $25,000 (D) $30,000 (E) $32,500

We know that there are x employees. Since the median salary is the 22nd salary, no two salaries are the same, and the 22nd salary is there in the list, there would be 21 salaries that are less than the 22nd salary and 21 salaries that are greater than the 22nd salary. This implies that there are 21 + 1 + 21 = 43 salaries in the list or there are a total of 43 employees. Thus, the average salary of the 43 employees = Total salary/Number of employees = $ 860, 000/43 = $20 B