1. If 12P + 3R + 4Q = 16, where P, Q and R are positive real numbers, then what is the maximum possible value of P³R³Q²

(a) 1

(b) 2

(c) 4

(d) 8

2. Out of the shirts produced in a factory, 15% are defective, while 20% of the rest are sold in the domestic market. If the remaining 8840 shirts are left for export, then the number of shirts produced in the factory is

(a) 13600

(b) 13000

(c) 13400

(d) 14000

3. In a village, the production of food grains increased by 40% and the per capita production of food grains increased by 27% during a certain period. The percentage by which the population of the village increased during the same period is nearest to

(a) 16

(b) 13

(c) 10

(d) 7

4. In an examination, the maximum possible score is N while the pass mark is 45% of N. A candidate obtains 36 marks, but falls short of the pass mark by 68%. Which one of the following is then correct?

(a) 201 ≤ N ≤ 242

(b) N ≥ 253

(c) N ≤ 200

(d) 243 ≤ N ≤ 252

5. A contractor did not have space in his garage for 8 of his trucks. He, therefore, increased the size of his garage by 50% which gave him space for 8 more trucks than he owned altogether. How many trucks did he own?

(a) 32 (b) 48

(c) 40 (d) 45

Solutions

1.

2. (b) Let total shirts produced = 100x

Defective = 15x

Rest = 85x

Shirts sold in domestic market = 17x

Remaining shirts = 68x

So, 68x = 8840

100x = 13000

3. (c) The required percentage 40/127 – 1 * 100 = 10%

4. (d) According to the question,

36 = (1-68/100)(45N/100)

36 = (32/100)(45N/100)

N = 250

Hence, 243 ≤ N ≤ 252

5. (c) Suppose the contractor had x trucks.

So, we have

x+8/x-8 = 3/2

So, x= 40

Daily Challenge

CAT Preparation – Day 1 : Arithmetic – Percentages

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