CAT - Numerical Ability - 2

CAT – Numerical Ability - 2

Find the value of ‘?’ in the following questions.

 
1. 3695.12 + 4458.02 - ? = 7592.14
a)  465                   b)651                     c) 575                    d)  561

Ans: (d)

2.      ? x 35 + 265 = 2680
a) 79                      b)63                       c)75                        d)  68

Ans: none of these (correct Answer 69)

  ? x 35 = 2680 - 265 = 2415
--> ? = 2415/35 = 69

3.  11 x (468 /26) = ? + 13
a) 175                                    b)185                     c) 211                    d) 201

Ans: (b)

11 x  (468/26) = 11 x 18 =198 -> ? + 13    ? = 198 – 13 = 185

4.       ?% of 550 - 12% of 150 = 125
a) 54                      b)44                       c)16                        d) 36                      e) none of these

Ans: (e)
X% of 550 – 12% of 150 = 125.  ->  x% of 550 – 18 = 125.  X% = 143 / 550 =26 (not in the choice)

5.     2234 + 84 - 1273 = ? + 123
a)922            b) 932           c) 822           d) 832           e) none of these

Ans: (a)

6.  In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
a) 1/10                  b) 2/5                    c) 2/7                     d) 5/7                    e) none of these

Ans:  (c)
There are 10 prizes and 25 blanks totalling 35. Probability of getting a prize is 10/35 -> 2/7

7.  Two dice are tossed. The probability that the total score is a prime number is:
a) 1/6                    b) 5/12                  c) 7/9                     d) none of these

Ans: (b)
A dice has six sides and the total possibilities when two dice are tossed is 6 x 6 = 36

The number of ways the total is a prime number is when the dice fall in the following manner 

{ (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3), (5, 2), (5, 6), (6, 1), (6, 5)}

Thus there are 15 possibilities of the sum being a prime number .

Hence the probability of getting a sum equal to prime number is 15/36 -> 5/12

8.  If Rs. 782 be divided into three parts, proportional to 1/2 : 2/3 : 3/4 , then the first part is:
a)Rs. 182                              b) Rs. 190             c) Rs. 196             d)Rs. 204

Ans: (d)
The ratio when simplified becomes 1/2 : 2/3 : 3/4 = 6 : 8 : 9.

Thus the first part is (782 x 6)/ 23 = Rs 204.00

9. A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
a) Rs. 500                             b) Rs. 1500          c) Rs. 2000           d) 3000                

Ans: (c)
This question needs no working. C gets Rs 1000 more than D and C gets one part more than D in the ratio. Thus we now know one part is equal to Rs 1000. B’ share is 2 parts. Ie 2 x 1000 = Rs 2000 

10. A can run 22.5 m while B runs 25 m. In a kilometre race B beats A by:
a) 100 m                               b) 25 m                 c) 50 m                  d) 111 1/9 m

Ans: 100 m
Another simple sum not requiring any working. In a race of 25 m B beats A by 2.5 m. So in a race of 100 m B will beat A by 10 m and in a kilometre race B will defeat A by 100 m.

11. If Rs. 10 be allowed as true discount on a bill of Rs. 110 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is:
a) Rs. 20                               b) Rs. 21.81         c) Rs. 22                d) Rs. 18.33

Ans: (d)
Let us assume the period as one year. Then at the end when the bill value is 110 a discount of 10 is allowed. This works out to a ate of interest of 10% p.a. So for twice the period the simple interest works out to Rs 20. If this amount is given as discount from the amount of Rs 110 then it works out to (20/120) x 110 = Rs 18.33

  
12. A man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. If the rate of interest is 10% per annum, the man:
a) gains Rs. 55                    b) gains Rs. 50                    c) loses Rs. 30                    d) gains Rs. 30

Ans: (b)
The watch is sold after one year at 10% interest. In other words if the watch was purchased at Rs. 100 then the sale price after one year was 110%. Now we have an equation 110% = Rs. 2200

Then 100 the cost price is equal to Rs. 2000. But the actual purchase price of the watch was Rs. 1950. Hence the gain in the sale is Rs. 2000 – Rs 1950 = Rs. 50.

13. Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 percent p.a. How much amount will Albert get on maturity of the fixed deposit?
a) Rs. 8600                           b) Rs. 8620          c) Rs. 8820           d) none of these

Ans: (c)  Apply the formula  P ( 1 + R/100 )ⁿ

14. The H.C.F. of 9/10 , 12/25 , 18/35 and 21/40 is:
a) 3/5                    b) 252/5               c) 3/1400              d) 63/700

Ans: (c)   (Apply the formula HCF of the numerators / LCM of the denominators)

  
15. Which of the following has the most number of divisors?
a) 99                      b) 101                    c) 176                    d) 182

Ans: (c)  

Divisors for 99 =  1, 3, 9, 11, 33, 99  -> 6 Nos  

Divisors for 101 = 1 x 101                 - > 2 Nos

Divisors for 176 = 1, 2, 4, 8, 11, 16, 22, 44, 88, 176  - > 10 Nos

Divisors for 182 = 1, 2, 7, 13, 182   - > 5 Nos