GRE
Practice Test 34
Previous Solution Next
N = 17 × 14 × 39 × 43 – 2
Remainder when N is divided b 6 2
  • Solution

    Using BODMAS rule N = (17 × 14 × 39 × 43) - 2

    Consider \(\frac{17 \times 14 \times 39\times 43}{6}\) = 17 × 7 × 13 × 43

    Which is an exact multiple of 6.

    ∴ (17 × 14 × 39 × 43) - 2 when divided by 6 gives a remainder of 4

1 Sociology, 1 Anthropology. 1 History and 1 Geography books can be arranged in n ways such that History and Geography books are always next to each other.
n 10
  • Solution

    History and Geography books can be held together as one unit.

    ∴ There are 3 units -

    I(H, G), IS, lA which can be arranged among themselves in 3! number of ways.

    Also the History and Geography books can be arranged among themselves in 2! number of ways.

    ∴ n=2! × 3!= 12

 

Product of all distinct prime factors of 52 Product of all distinct prime factors of 63
  • Solution

    52 = 2 × 2 × 13

    Distinct primes are 2 and 13.

    ∴ Col. A = 2 × 13 = 26

    63 = 3 × 3 × 7

    Distinct primes are 3 and 7.

    ∴ Col. B = 3 × 7 = 21

x y + z
  • Solution

    Let ∠ABC = C

    y + z = C

    Now we have to decide which angle is greater x or c. But it will depend on the position of C.

x>0
(10)2x-1 x(10)-2
  • Solution

    Col. A = \(\frac{100}{x}\),Col.B =\(\frac{x}{100}\)

    Let x = 0.5

    ∴ Col. A > col. B

    Let x = 100, Col. A = Col. B

    Let x = 200, Col. A < Col. B

y is a positive integer. x2 = y2 + 5
x y
  • Solution

    Let Y = 2 ∴ y2 = 4

    ∴ x2 = 9 ∴ x = ±3

    If x = +3 Ans: (A)

    If x = -3 Ans: (8)

A garden measuring 64 m by 52 m is to be surrounded by a flagstone walkway 6 m wide. Each stone is rectangular and has dimensions 3m × 4m
Number of stones needed to cover the walkway 120
  • Solution

    Area of the walkway = (76 × 64) - (64 × 52)

    = 64 (76 - 52) = 64 × 24 m2

    ∴ Number of stones needed

    =\(\frac{64\times 24}{4\times 3}\)=16 × 8 = 128

According to a recent survey, 36% of the 3000 employees at company k were discontented with their job. Of this group, 25% had worked at the company for at least 10 years. 45% of all the employees have worked at the company for at least 10 years.
The number of people who had worked at least 10 years and did not respond that they were discontented with the jobs 800
  • Solution

    36% of 3000 = 1080 employees are discontented. 25% of 1080 = 270 have been working for last 10 years.

    Total number of employees working for last 10 years = 45% of 3000 = 1350

    ∴ Col. A = 1350 - 270 = 1080 employees did not respond that they were discontented

    ∴ Col. A = 1080, Col. 8 = 800

Last year, ‘m’ employees of a bank divided ‘k’ dollars profit evenly among themselves, ‘n’ people join the bank during the year.
The additional profit in $, the bank must now make, so that amount of profit per employee remains same \(\frac{kn}{m}\)
  • Solution

    Last year, each employee got k⁄m dollars.

    This year, the bank has m + n employees.

    Profit per employee = k⁄m

    ∴ Total profit this year must be k⁄m × (m + n)

    = k + \(\frac{kn}{m}\)

    ∴ Additional profit = \(\frac{kn}{m}\)

At a TV dealership, total profit from sales increased by 10% over the previous year, while the number of TV sets sold decreased by 10% over the previous year.
The % increase in profit per TV set over the previous year 22
  • Solution

    Assume that, initially the dealership sold 100 TV sets at a $100 profit per TV set.

    ∴ Total profit = 100 × 100 = $10000

    Next year, it sold 90 TV sets and earned a total profit of 10000 × 1.1 = $11000

    ∴ Selling price of 1 TV = \(\frac{11000}{90}\) = \(\frac{1100}{9}\) = 122.22

    ∴ %increase = 22.22% ∴ Col. A > Col. 8

Attempted

0

Correct

0

Wrong

0

Complete
Quantitative Comparison
Attempted
Wrong
Correct