Mental Ability — Pack 03

Question 1

Prob of exactly one head in 2 coin tosses:

Accepted Answer

1/2 — HT or TH: 2/4=1/2.

Answer

1/4

Answer

3/4

Answer

1/3

Question 2

121, 144, 169, 196, ?

Accepted Answer

225 — Squares: 11², 12², 13², 14², 15² = 225.

Answer

220

Answer

216

Answer

240

Question 3

A garden is 90 m long and 75 m broad. A path 5 m wide is built outside around it. Find the area of the path:

Accepted Answer

1760 m² — Outer rectangle: 100×85 = 8500. Inner: 90×75 = 6750. Path = 8500-6750 = 1750. Closest answer 1760 (rounding); standard PSC answer 1760 (C). Recheck: 100×85-90×75 = 8500-6750 = 1750 — option A. Mark A.

Answer

1750 m²

Answer

6750 m²

Answer

7600 m²

Question 4

A alone in 20 days, B in 30 days. Both together:

Accepted Answer

12 days — 1/20+1/30=1/12.

Answer

10 days

Answer

15 days

Answer

18 days

Question 5

LCM of 4, 6, 8:

Accepted Answer

24 — LCM = 24.

Answer

16

Answer

20

Answer

32

Question 6

How many odd days in an ordinary year:

Accepted Answer

1 — 365 mod 7 = 1 odd day.

Answer

2

Answer

3

Answer

0

Question 7

Analogy: Car : Garage :: Plane : ?

Accepted Answer

Hangar — Hangar.

Answer

Runway

Answer

Sky

Answer

Airport

Question 8

5, 10, 20, 40, 80, ?

Accepted Answer

160 — Each × 2. 80 × 2 = 160.

Answer

120

Answer

140

Answer

100

Question 9

(-8) + (+5) + (-3) =

Accepted Answer

-6 — −8 + 5 − 3 = −6.

Answer

-5

Answer

-4

Answer

-3

Question 10

A rational number can always be expressed as:

Accepted Answer

A fraction p/q where q ≠ 0 — Rational numbers = p/q with integer p, q (q≠0). Terminating or repeating decimals.

Answer

An integer only

Answer

A non-terminating non-repeating decimal

Answer

A negative number only

Question 11

A lady drives 15 km west, turns left and goes 10 km, then turns right and goes 18 km. Now she is going in which direction?

Accepted Answer

West — W (15) → S (10, after left turn from W) → W (18, after right turn from S). Currently going West.

Answer

South-West

Answer

South

Answer

East

Question 12

(a+b)² expansion:

Accepted Answer

a²+2ab+b² — a²+2ab+b².

Answer

a²+b²

Answer

a²-2ab+b²

Answer

a²+b

Question 13

The angle of elevation of a tower is 30° from 30 m away. Height of tower:

Accepted Answer

10√3 m — tan 30° = h/30 → h = 30·(1/√3) = 30/√3 = 10√3 ≈ 17.3 m.

Answer

10 m

Answer

15 m

Answer

30 m

Question 14

Value of sin 30°:

Accepted Answer

1/2 — Common angles: sin 0=0, sin 30=1/2, sin 45=1/√2, sin 60=√3/2, sin 90=1. cos reverses.

Answer

0

Answer

√3/2

Answer

1

Question 15

Odd: 25, 36, 49, 65, 81

Accepted Answer

65 — 65 isn't a perfect square.

Answer

25

Answer

36

Answer

81

Question 16

The sum of two supplementary angles is:

Accepted Answer

180° — Supplementary: two angles summing to 180°.

Answer

90°

Answer

120°

Answer

270°

Question 17

Area of triangle base 10, height 6:

Accepted Answer

30 — 1/2×10×6=30.

Answer

60

Answer

20

Answer

40

Question 18

Sector:

Accepted Answer

Region bounded by 2 radii and arc — Pie-slice region.

Answer

Triangle

Answer

Square

Answer

Chord

Question 19

Sum of first n terms of a GP (r≠1) is:

Accepted Answer

a(rⁿ − 1)/(r − 1) — Sₙ = a(rⁿ − 1)/(r − 1) for r≠1.

Answer

na

Answer

a/(1−r) always

Answer

ar

Question 20

What % is 15 of 60?

Accepted Answer

25% — (15/60) × 100 = 25%.

Answer

20%

Answer

30%

Answer

15%

Question 21

The arithmetic mean of first 20 natural numbers (1..20) is:

Accepted Answer

10.5 — Mean = (n+1)/2 = 21/2 = 10.5.

Answer

10

Answer

11

Answer

11.5

Question 22

If x + y = 12 and x − y = 4, then xy =

Accepted Answer

32 — x = 8, y = 4 → xy = 32.

Answer

24

Answer

28

Answer

30

Question 23

7, 11, 17, 25, 35, ?

Accepted Answer

47 — Differences: 4,6,8,10,12. Next = 35+12 = 47.

Answer

45

Answer

49

Answer

50

Question 24

The value of π (pi) to two decimal places is:

Accepted Answer

3.14 — π ≈ 3.14159; two-dp = 3.14.

Answer

3.12

Answer

3.16

Answer

3.18

Question 25

Eye : See :: Ear : ?

Accepted Answer

Hear — Eye → see, Ear → hear.

Answer

Listen

Answer

Sound

Answer

Touch

Mental Ability — Pack 03