GATEWAY TO CGL MAINS 2015 : Quant Quiz

1.The sum of first 20 odd natural numbers is equal to : 

(1) 210 

(2) 300 

(3) 400 

(4) 420

2.What number should be subtracted from both term of the ratio 15 : 19 in order to make it 3 : 4? 

(1) 9 

(2) 6 

(3) 5 

(4) 3

3.A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?

(1) Rs. 8000 

(2) Rs. 8500

(3) Rs. 9000 

[4] Rs. 7500

4.A, B and C rent a pasture. A puts in 10 oxen for 7 months, B  12 oxen for 5 months and C 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175/per, how much must C pay as his share of rent?

(1) Rs. 45 

(2) Rs. 50

(3) Rs. 55 

(4) Rs. 60

5.A reduction of 20% in the price of oranges enables a man to buy 5 oranges more for Rs. 10/ -. The price of an orange before reduction was: 

(1) 20 paise 

(2) 40 paise

(3) 50 paise 

(4) 60 paise

6.In an examination, a student who gets 20% of the maximum marks fails by 5 marks. Another student who scores 30% of the maximum marks gets 20 marks more than the pass marks. The necessary percentage required for passing is :

(1) 32% 

(2) 23%

(3) 22% 

(4) 20%

7.If 3 men or 6 women can do a piece of work in 16 days. in how many days can 12 men and 8 women do the same piece of  work? 

(1) 4 days 

(2) 5 days

(3) 3 days 

(4) 2 days

8.On what sum does the difference between the compound in  interest and the simple interest for 3 years at 10% is Rs. 31 ?

(1) Rs. 1500 

(2) Rs. 1200

(3) Rs. 1100 

(4) Rs. 1000

9.A builder borrows Rs. 2550 to be paid back with compound interest at the rate of 4% per annum by the end of 2 years in  two equal yearly instalments. How much will each instalment be ?

(1)Rs. 1352 

(2)Rs. 1377 

(3)Rs. 1275 

(4)Rs. 1283

10.At what percent per annum will Rs. 3000/ - amount to Rs. 3993 in 3 years if the interest is compounded annually?  

(1) 9% 

(2) 10%

(3) 11% 

(4) 13%

ANSWERS AND SOLUTION
1.(3) Series of first 20 odd natural numbers is an arithmetic progression with 1 as the first term and the common difference 2.
Sum of the n terms in arithmetic progression is given by.
Sn = 1/2 n[2a + (n-1)d]
Where a : First term
d : common difference
so (S)20 = 1/2 * 20 {2 * 1) + (20 – 1) * 2}
= 10[2 + 38] = 10 * 40 = 400

2.(4) Let x be subtracted from each term of 15/19
so (15 – x)/(19 – x) = 3/4
=> 57 – 3x = 60 – 4x
=> x = 3

3.(3) A’s investment of Rs. 3500 is for 12 months
B’s investment (let it be Rs. x) is for 7 months only.
At the end of the year the profit is divided in the ratio 2 : 3 and it must be equal to the ratio of the product. (Amount * time)
(12 * 3500)/7x = 2/3
Or x = (12 * 3500)/7 x 3/2
Or x = 9000
so B’s investment is Rs. 9000.

4.(1) Share of rent = (number of oxen x time)
A : B : C  = (10 * 7) : (12 * 5) : (15 * 30)
A : B : C = 70 : 60 : 45
A : B : C = 14 : 12 : 9
C’s share of rent
= 9/ (14 + 12 + 9) * 175 = 9/35 * 175 = 45
C’s share of rent is Rs. = 45

5.(3) 20% of Rs. 10
= 20/100 * Rs. 10 = Rs. 2
Reduced price of 5 oranges
= Rs. 2
so Reduced price of 1 orange
= Rs. 2/5 = 200/5 paise = 40 paise
Original price of 1 orange
 = 40/(1 – 0.20) = 40/0.8 = 400/8 = 50 paise

6.(3) Let the maximum marks be x.
According to question.
20% of (x + 5) = 30% of (x – 20)
(30 – 20)% of x = 25
x = (25 * 100)/10 = 250
so Pass marks
= 20% of 250 + 5 = 55
so % Pass marks = 55/250 * 100 = 22%

7.(3) 3m = 6w
so m = 2w
12m + 8w = (12 * 2w) + 8w = 32w
so 6 women can do the work in 16 days.
so 32 women can do the work (16 * 6)/32 = 3 days
8.(4)
9.(1)
10.(2)