Mathmetics

ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams

Q11.
The L.C.M of two numbers is 45 times their H.C.F. If one of the number is 125 and the sum of H.C.F and L.C.M is 1150, the other number is - 
1) 215 2) 220
3) 225 4) 235
5)None of these
Answer : 225
Explanation : Given that, 45 H.C.F = L.C.M   and  
H.C.F + L.C.M = 1150 
or H.C.F + 45 H.C.F = 1150
or 46 H.C.F = 1150
or H.C.F = 1150/46 =25
So, L.C.M = 25 X 45 = 1125
Now, we can get 125 X x = 25 X 1125
or   x =  (25 X 1125) /125 = 225

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Q12.
What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ?
1) 196 2) 630
3) 1260 4) 2520
5)None of these
Answer : 630
Explanation :
L.C.M. of 12, 18, 21 30                
     = 1260.      
So, required number = (1260 ÷ 2)   = 630.
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Q13.
What is the least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder ?
1) 1677 2) 1683
3) 2523 4) 3363
5)None of these
Answer : 1683
Explanation :
L.C.M. of 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 x 2 + 3) = 1683.
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Q14.
The sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively. What should be the sum of the reciprocals of the numbers ?
1) 55/601 2) 12/55
3) 11/120 4) 11/112
5)None of these
Answer : 11/120
Explanation :
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Q15.
The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
1) 279 2) 283
3) 308 4) 318
5)None of these
Answer : 308
Explanation : We know that H.C.F x L.C.M = Product of two numbers
So,other number = (11 x 7700)/275 = 308.
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Q16.
The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
1) 1677 2) 1683
3) 2523 4) 3363
5)None of these
Answer : 1683
Explanation :
        L.C.M. of 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 x 2 + 3) = 1683.
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Q17.
What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30  ?
1) 196 2) 630
3) 1260 4) 2520
5)None of these
Answer : 630
Explanation :
        L.C.M. of 12, 18, 21 30 = 1260.      
    Required number = (1260 ÷ 2) = 630.

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Q18.
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:
1) 1 2) 2
3) 3 4) 4
5)None of these
Answer : 2
Explanation :
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.
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Q19.
 The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:
1) 20 2) 23
3) 169 4) 400
5)None of these
Answer : 23
Explanation :
Let the numbers be x and y.
Then, xy = 120 and x2 + y= 289.
(x + y)2 = x2 + y+ 2xy = 289 + (2 x 120) = 529
x + y = 23.
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Q20.
The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:
1) 101 2) 107
3) 111 4) 185
5)None of these
Answer : 111
Explanation :
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.
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