# SSC Quantitative Aptitude Questions (Day-78)

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1) How many factors of 108 is/are prime number?

(a) 2

(b) 3

(c) 5

(d) 6

Direction (2-3): Which of the following expression(s) is/are true?

2) I) √5 + √5 > √2 + √8

II) √3 + √7 > √2 + √8

III) √5 + √5 > √3 + √7

(a) Only I

(b) Only I and III

(c) Only II

(d) All expressions are true

3) I)
337 is a prime number.

II) The number 12 has 6 positive factors.

III) 32724 is completely divisible by 9.

(a) Only I

(b) Only I and II

(c) Only II and III

(d) All expressions are true

4) (a)∛8

(b) √(2&4)

(c) √(6&64)

(d) All are equal

5) What is the value of (1004)2 – (998)2?

(a) 11012

(b) 12012

(c) 120012

(d) 1212

6) A and B together can complete a work in 15 days. They started together but after 5 days A left the work. If the remaining work is completed by B in 15more days, then A alone can complete the entire work in how many days?

(a) 25

(b) 50

(c) 35

(d) 45

7) P is 20% more efficient than Q. If Q alone can finish a work in 10 days, then in how many days P alone will finish the work?

(a) 8 1/3

(b) 8.5

(c) 9

(d) 12

8) The ratio of marked price and cost price of an article is 6 : 5. If 15% discount is given, then how much is the profit (in percent)?

(a) 4

(b) 0.2

(c) 2

(d) 1

9) Out of the following, which is the best discount for a customer?

I) 50% + 50% off

II) 60% + 40% off

III) 70% + 30% off

(a) Only I and IV

(b) Only II

(c) Only I, II and III

(d) Only III

10) (a) 3

(b) 2

(c) 4/3

(d) 7/3

108 ⇒ 2², 3³

Two factors are prime.

√7 + √3 & √5 + √5  and √2 + √8

Squaring all terms

10 + 2√21, 10+2√25, 10 + 2√16

Hence

√5 + √5 > √7 + √3 > √2 + √8

I — 337 is a prime

II — 12 = 2².3

(3 × 2) = 6 factors

III — 3 + 2 + 7 + 2 + 4 = 18

∵ sum of digits is divisible by 9

Hence no. is divisible 9.

∛8 √(2&4)√(6&64)

8 = 2³, 4 = 2², 64 = 2⁶

Hence all are equal.

(1004)² – (998)²

= (1004 –998) (1004 + 998)

= 12012

In 5 days A & B will work ⅓ of the given work

& to finish ⅔rd of the given work B takes = 15 days

Hence, B will finish in = 45/2 days

1/A = 1/15 – 2/45

= (3–2) / 45

= 1/45

A = 45 days

Suppose if Q work 5 units per day

Then P will do = 6 units per day (20% efficient)

Total work = 10 × 5 ⇒ 50 units

P will finish in 50/6 days

MP/CP = 6/5

Let MP = 600 and & C.P. = 500

For 15% discount ⇒ 600× 15/100 = 90 Rs.

S.P. = 600 – 90 = 510

Profit % = (510 –500) / 500 × 100%

= 2%  