Quantitative Aptitude Quiz : 4 March 2021

Updated Fri, 05 Mar 2021 02:02 PM IST

Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

a) 4                              b) 5                              c) 6                              d) 7
 
Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)
 = H.C.F. of 48, 92 and 140 = 4.

 
The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14.

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The larger of the two numbers is: 


a) 296                          b) 322                          c) 256                          d) 338

Clearly, the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322. 


Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together? 
a) 12                          b) 16                            c) 8                                 d) 20
 
L.C.M. of 2, 4, 6, 8, 10, 12 is 120.
So, the bells will toll together after every 120 seconds (2 minutes).
In 30 minutes, they will toll together = 30/2 + 1 = 16 times

 
Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is: 

a) 10                           b) 8                                 c) 6                                    d) 4
 
N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
  = H.C.F. of 3360, 2240 and 5600 = 1120.
Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4

 
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is: 

a) 9400                       b) 9200                             c) 9600                              d) 9800
 
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600. 


The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is: 
a)  111                         a) 101                          c) 91                            d) 121
 
Let the numbers be 37a and 37b.
Then, 37a x 37b = 4107
ab = 3.
Now, co-primes with product 3 are (1, 3).
So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).
Greater number = 111.


Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is: 

a) 80                            b) 40                            c) 120                          d) 60

Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or x = 40.
 The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40.

 
The G.C.D. of 1.08, 0.36 and 0.9 is: 

a) 0.36                         b) 0.18                         c) 0.54                         d) 0.72

Given numbers are 1.08, 0.36 and 0.90.   H.C.F. of 108, 36 and 90 is 18,
H.C.F. of given numbers = 0.18. 

 
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is: 
a) 2                              b) 4                              c) 1                              d) 3
 
Let the numbers 13a and 13b.
Then, 13a x 13b = 2028
 ab = 12.
Now, the co-primes with product 12 are (1, 12) and (3, 4).
So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).
Clearly, there are 2 such pairs.
 

The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is: 

a) 364                          b) 384                          c) 344                          d) 404
 
L.C.M. of 6, 9, 15 and 18 is 90.
Let required number be 90k + 4, which is multiple of 7.
Least value of k for which (90k + 4) is divisible by 7 is k = 4.
Required number = (90 x 4) + 4   = 364.
 

 
 
 
 
 
 
 
 
 
 
 

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