Gate Way To CGL Mains : Quant Quiz

1.Which of the following is the most attractive for a customer? 

(a)A single discount of 20% 

(b)Two successive discounts of 10% each. 

(c)A 5% discount followed by a 15% discount 

(d)A 15% discount followed by a 15% discount. 

2.A car covered 1/10 th of a certain distance at a speed of 12 km/hr, 1/5 th  of the distance at a speed of 37.5 km/hr and the remaining distance at a speed of 30 km/hr. Find the average speed of the car for the entire journey. 

(a) 28 4/37 km/hr

(b) 26 1/2 km/hr

(c) 29 7/37 km/hr

(d) 27 1/37 km/hr

3.If X7X625 is divisible by 11 where X is a single digit number, then the value of X is _____ .

(a) 9 

(b) 8 

(c) 7 

(d) 6 

4.Find the least positive integer that should be added to 3017 * 3018 so that the result is a perfect square. 

(a) 3017 

(b) 3018 

(c) 3016 

(d) 3019 

5.A sum of money was invested at a certain rate of compound interest, interest being compounded half yearly. The sum doubles in 3 years. Find the time that the sum would take to quadruple. 

(a) 5 years 

(b) 6 years 

(c) 7 years 

(d) 8 years 

6.The ratio of the radii of two right circular cylinders is 3 : 4. The ratio of the  heights of the first and the second cylinders is 3 : 4. Find the ratio of the total surface areas of the first and the second cylinders. 

(a) 9/16 

(b) 16/9 

(c) 3/4 

(d) 4/3 

7.Amar invested a total Rs. 84, 100 in the names of his two sons when they were ages 11 years and 13 years. Each sum was invested at 5% p.a compound interest. The sums invested were such that each sum would amount to the same value when the sons become 18 years old. Find the sum invested in the name of the older son. 

(a) Rs. 43, 200 

(b) Rs. 45, 600

(c) Rs. 46, 500

(d) Rs. 44, 100

8.P and Q can complete a job in 8 days and 10 days  respectively. They worked on alternate days and completed the job. Q worked on the first day. Find the time taken to complete the job. 

(a) 8  4/5 days 

(b) 9 days

(c) 9 1/5 days

(d) 9 2/5 days

9.A and B run around a circular  track of length 720 m at speeds of 12 m/s and 18 m/s respectively. They start at the same time from the same point in opposite directions. After how long will they meet for the first time at the starting point? 

(a) 100 sec 

(b) 130  

(c) 110 sec 

(d) 120 sec 

10.The ratio of two natural numbers is 5 : 6. If the number is added to both the numbers, the ratio becomes 7 : 8. If the larger number exceeds the smaller number by 10, find the number added. 

(a) 5 

(b) 10 

(c) 20 

(d) 30

ANSWERS AND SOLUTION 
1.(a) 
2.(d) Let the distance be D km
Total travel time
= (D/10)/12 + (D/5)/(75/2) + (D- (D/10+D/5))/30
=D/120+2D/375+7D/300=111D/3000
Average speed = D/((111D/3000) )=1000/37=27 1/37 km/hr
3.(b) If X7X625 is divisible by 11,
difference (X + X + 2,  7 + 6 + 5) must be divisible by 11.
Difference [2X + 2), (18)] must be divisible by 11.
Let us go by the choices Choice 1 : 2x + 2 = 20.
so Difference = 2 which is not divisible by 11.
Choice 2 : 2X + 2 = 18  .
so Difference = 0 which is divisible by 11.
so X = 8 is  possible
Each choice contains a unique value.
x = 8 is the only possible answer.
 4.(b) Let the least positive integer that should be added be x.
3017 * 3018 + x must be a perfect square.
3017  * 3018 + x = 3017 * (3017 + 1) + x
= (3017)^2 + 3017 + x
This must be > (3017)^2 ( x > 0)
so (3017)^2  + 3017 + x ≥ (3018)^2
3017 + x ≥ (3018)^2 – (3017)^2 = (3018 – 3017) (3018 + 3017)
3017 + x ≥ 6035
X ≥3018
As x is the least positive integer, x = 3018.
 5.(b) 
6.(a) Let the radii of the first and the second cylinders be
3x and 4x respectively. Let the ratio of the heights of the first and the second cylinders be 3y and 4y respectively.
Ratio of the total surface areas of the first and the second cylinders.
= 2π (3x)(3x+3y):2π(4x)(4x+4y)
= 3/4  × 3(x+y)/4(x+y)   = 9/16
7.(d) 
8.(b) 
9.(d)Time taken to meet at starting point
= LCM of= ((length track )/(speed of A ),(length of track)/(speed of B ))
Time taken to meet = LCM (720/12 720/18)
LCM (60 ,40) = 120 sec.
10.(c)