Mock Test-4 (Paper-1) (Question 101-125)

Total Questions: 25

11. Two numbers are such that the sum of twice the first number and thrice the second number is 36 and the sum of thrice the first number and twice the second number is 39. Which is the smaller number?

Correct Answer: (e) None of these
Solution:Let the numbers be x and y.

According to the question,

2x + 3y = 36 ....... (i)

3x + 2y = 39 ....... (ii)

By equation (i) × 3 - (ii) × 2,

6x + 9y - 6x - 4y = 108 - 78

⇒ 5y = 30 ⇒ y = 30/5 = 6

From equation (i), we have,

2x + 3 × 6 = 36

⇒ 2x = 36 - 18 = 18

⇒ x = 18/2 = 9  and, y = 6

∴ The smaller number = 6

12. The six-digit number 5 A B B 7 A is a multiple of 33 for digits A and B. Which of the following could be possible value of A + B?

Correct Answer: (b) 9
Solution:A number is divisible by 33 if it is divisible by 3 and 11 both

For divisibility by 11,

∴ 5 + B + 7 = A + B + A

∴ 2A =12 ⇒ A = 6

∴ For divisibility of 5 6 B B 7 6 by 3,

Sum of its digit should be divisible by 3

5 + 6B + B + 7 + 6 = 24 + 2B, B = 3

∴ Number = 563376

∴ A + B = 6 + 3 = 9

13. In an election 10% of the voters on the voter's list did not cast their votes and 60 voters cast their ballot paper blank. There were only two candidates. The winner was supported by 47% of all the voters in the list and he got 308 votes more than his rival. The number of voters on the list was

Correct Answer: (b) 6200
Solution:

14. Seema's present age is four times her son's present age and four-seventh of her father's present age. The average of the present age of all three of them is 32 years. What is the difference between the Seema's son's present age and Seema's father's present age?

Correct Answer: (b) 48 years
Solution:Let Seema's son's present age = x years

∴ Seema's present age = 4x years

∴ Seema's father's present age

= 4x × 7/4 = 7x years

Now x + 4x + 7x = 32 × 3

⇒ 12x = 96

⇒ x = 96/12 = 8

∴ Required difference

= 7x - x = 6x = 6 × 8 = 48 years

15. Arun buys one kilogram of apples for 120 and sells it to Swati gaining 25%. Swati sells it to Divya and Divya again sells it for 198, making a profit of 10%. What is the profit percentage made by Swati?

Correct Answer: (b) 20%
Solution:

16. Ratio of the earnings of A and B is 4 : 7 respectively. If the earnings of A increase by 50% and the earnings of B decrease by 25% the new ratio of their earnings becomes 8 : 7 respectively. What are A's earnings.?

Correct Answer: (d) ₹ Data inadequate
Solution:Let the earnings of A and B be ₹ 4x and 7x respectively.

After 50% increase, A's earnings = 150% of 4x

After 5% decrease,

B's earning = 75% of 7x

Ratio = 150% of 4x : 75% of 7x = 8 : 7

But their total earnings are unknown.

Hence A's earnings can't be known.

17. A principal of ₹ 10,000, after 2 years compounded annually, the rate of interest being 10% per annum during the first year and 12 % per annum during the second year (in rupees) will amount to :

Correct Answer: (b) ₹ 12,320
Solution:

18. A solid is in the form of a right circular cylinder with hemispherical ends. The total length of the solid is 35 cm. The diameter of the cylinder is 1/4 of its height. The surface area of the solid is (Take π = 22/7)

Correct Answer: (d) 770 cm²
Solution:

Total surface of area the solid

= (2πrh + 2 × 2πr²) sq. cm.

= 2πr(h + 2r) sq. cm.

= 2 × 22/7 × 7/2 × (28 + 2 × 7/2) sq.cm

= 2 × 22/7 × 7/2 × 35 sq.cm = 770 sq.cm

19. What should come in place of question mark (?) in the following number series?

119, 13, 15, 25, 55, 123, ?

Correct Answer: (d) 253
Solution:

20. How many words can be formed from the letters of the word SIGNATURE so that the vowels always come together?

Correct Answer: (e) None of these
Solution:The word SIGNATURE consists of nine letters comprising four vowels (A, E, I and U) and five consonants (G, N, R, T and S). When the four vowels are considered as one letter, we have six letters which can be arranged in ⁶P₆ ways i.e. 6! ways. Note that the four vowels can be arranged in 4! ways.

Hence required number of words

= 6! × 4! = 720 × 24 = 17280