LIC AAO | QUANT QUIZ - 17 | S W A G

Directions (Q. 1-10): Study the following information carefully and answer the given questions

1). In a class there are 8 boys and 5 girls. In how many ways they can sit in row so that no two girls sit together?
a) (9! × 8!) / 5!
b) (9! × 8!) / 4!
c) 9! / 5!
d) 8! / 5!
e) 8! / 4!

2). A bag contains 5 red, 4 white, 3 black balls. 3 balls are drawn randomly. The probability of the balls drawn contains no red ball is -
a) 24 / 91
b) 12 / 65
c) 7 / 44
d) 33 / 91
e) 7 / 35

3). A sum was put at simple interest at a certain rate for 5 years. Had it been put at 5 % higher rate, it would have fetched Rs. 500 more. What is the sum?
a) Rs. 2000
b) Rs. 2400
c) Rs. 2500
d) Rs. 3200
e) Rs. 4400

4). What is the difference between the compound interest and the simple interest for the sum Rs. 16000 at 5% p.a for 2 years?
a) Rs.80
b) Rs.60
c) Rs.54
d) Rs.40
e) Rs.35

5). How much water must be added to a flask which contains 25 litres of milk at a cost price of Rs.8 per litre so that the cost of milk reduces to Rs.5 per litre?
a) 12 litres
b) 15 litres
c) 16 litres
d) 18 litres
e) 20 litres

6). Khalid left for Kanpur from Aligarh at 9.30 am. He travelled at the speed of 60 km/hr for 2 hours 15 minutes. After that the speed was reduced to 40 km/hr. If the distance between the two cities is 285 km, at what time did Khalid reach Kanpur?
a) 3.30 pm
b) 3.00 pm
c) 2.30 pm
d) 4 pm
e) None of these

7). If a clock numbered up to 12 strikes once at 1 o’ clock twice at 2 o’ clock, and so on, how many times does it strike in a week?
a) 1092
b) 546
c) 156
d) 168
e) None of these

8). A natural number is selected randomly and is divided by 9. What is the probability that the remainder is not an even number?
a) 5 / 8
b) 4 / 9
c) 1 / 2
d) 3 / 8
e) None of these

9). An equilateral triangle is cut up into smaller equilateral triangles with side 1 / 6 of the original. Find the number of triangles thus formed.
a) 216
b) 6
c) 36
d) 3
e) Can’t say

10). A shopkeeper purchased an article at 12% discount on marked price. The shopkeeper sold the same article for Rs.2000 and earned a profit of 13(7 / 11)%. Find the marked price of the article.
a) Rs.1760
b) Rs.2200
c) Rs.2500
d) Rs.2000
e) None of these


#Answers:

Solution:

1). Girls × B × B × B × B × B × B × B × B ×
8 boys can be seated in a row in 8! Ways.
For 5 girls there are 9 places so that no two girls sit together. So they can be seated in 9P5 ways.
∴ Total = 9P5 × 8! = (9! / 4!) × 8!  
Answer: b)

2). n(S) = 12C3 = [(12 × 11 × 10) / (3 × 2)] = 220
3 balls can be selected from 4 white and 3 black balls in 7C3 ways.
n(E) = 7C3 = [(7 × 6 × 5) / (3 × 2)] = 35
∴ P(E) = (35 / 220) = (7 / 44)
Answer: c)

3). Let the sum be x and original rate y% p.a
∴ new rate = (y + 5)%
{[x(y + 5) × 5] / 100} – {[x(y) × 5] / 100} = 500
=> ((xy + 5x) / 20) – (xy / 20) = 500
=> 5x / 20 = 500
∴ x = 500 × 4 = 2000
Answer: a)

4). Difference = 16000 × (5 / 100)2
= 16000 × [25 / (100 × 100)] = (16000 / 400) = 40
Answer: d)

5). Quantity of water = 25[(8 – 5) / 5] = (25 × 3) / 5 = 15 litres
Answer: b)

6). Khalid covers in 2 hrs 15 min the distance of 60 × (9 / 4) = 135 km
Remaining distance = 285 – 135 = 150 km
Time taken to cover this distance = 150 / 40 = 3hrs 45 min
So, Khalid reaches at Kanpur = 9.30 + 2.15 + 3.45 = 3.30 pm
Answer: a)

7). A week has 7 days and a day has 24 hrs divided into two equal rounds of 12 hrs each.
So, the required no. = 7 × 2 × (1 + 2 + 3 + …. + 12)
= (7 × 2 × 12 × 13) / 2 = 1092
Answer: a)

8). When a natural no. is divided by 9, the remainder may be 0 or 1, or 2 or 3 … or 8.
So, n(S) = 9
E (the remainder is not an even no.) = {1, 3, 5, 7} = 4
∴ P(E) = n(E) / n(S) = 4 / 9
Answer: b)

9). Reqd no. of triangles formed = [(√3 / 4) × a2] / [(√3 / 4) (a / 6)2] = 36
Answer: c)

10). CP of the article = 2000 × (22 / 55) = Rs. 1760
MP of the article = (1760 / 88) × 100 = Rs.2000

Answer: d)