Classical

Numbers & Algebra - Numbers and Algebra MCQ

21:  

Average age of a committee of seven trustees is the same as it was five years ago, a younger man having been substituted for one of them. How much younger was he then trustee whose place he took?

A.

32 years

B.

35 years

C.

33 years

D.

34 years

 
 

Option: B

Explanation :

Increase after 5 years should have been 7 x 5 = 35 years.
But since average remains same, diference in their age is 35 years.


22:  

What is the least number which must be subtracted from 1936 so that the remainder when divided by 9, 10, 15 will leave in each case the same remainder 7?

A.

32

B.

53

C.

46

D.

39

 
 

Option: D

Explanation :

L.C.M. of 9, 10 and 15 = 90
∴ 1936 = 90 x 21 + 46 (Remainder).
But a part of this remainder is 7.
39 should be subtracted from 1936.


23:  

What is the maximum sum of the series 60, 58, 56, 54, 52, ?

A.

840

B.

880

C.

930

D.

1120

 
 

Option: C

Explanation :

Since d = -2, maximum sum of the series will be sum of all the positive terms.
Least positive term of the series is 2 or 0 (both giving equal sum)
Let, 2 be the nth term
2 = 60 + (n 1) - 2 
=> n = 30
Required sum = 30/2 (60 + 2) = 930


24:  

What is the least number which on being divided by 12, 21 and 35 will leave in each case the same remainder 6?

A.

210

B.

414

C.

420

D.

426

 
 

Option: D

Explanation :

L.C.M. of 12, 21 and 35 = 420 
∴ Number required = 420 + 6 = 426


25:  

Six men A, B, C, D, E, F agree with a seventh man G to provide a sum of money among them. A, B, C, D, E, F are to subscribe Rs.10 each, and G is to pay Rs.3 more than the average of the seven. What is the whole sum to be provided?

A.

Rs.73.50

B.

Rs. 74

C.

Rs. 73

D.

Rs. 72.50

 
 

Option: A

Explanation :

let average of the seven men be x
∴ x = (10x6+(x+3)) / 7
=> 60 + x +3 = 7x
=> x = 63/6 = 10.5
Toal amount = 10.5 x 7 = 73.5




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