Mathmetics
ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams
Q541. 

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
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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Q542. 

1)  1677  2)  1683 
3)  2523  4)  3363 
5)  None of these 
Answer : 1683
Explanation :
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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Q543. 

1)  196  2)  630 
3)  1260  4)  2520 
5)  None of these 
Answer : 630
Explanation :
Explanation :
L.C.M. of 12, 18, 21 30 = 1260.
Required number = (1260 ÷ 2) = 630.
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Q544. 

1)  1  2)  2 
3)  3  4)  4 
5)  None of these 
Answer : 2
Explanation :
Explanation :
Let the numbers 13a and 13b.
Then, 13a x 13b = 2028
ab = 12.
Now, the coprimes 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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Q545. 

1)  20  2)  23 
3)  169  4)  400 
5)  None of these 
Answer : 23
Explanation :
Explanation :
Let the numbers be x and y.
Then, xy = 120 and x^{2} + y^{2 }= 289.
(x + y)^{2} = x^{2} + y^{2 }+ 2xy = 289 + (2 x 120) = 529
x + y = 23.
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Q546. 

1)  101  2)  107 
3)  111  4)  185 
5)  None of these 
Answer : 111
Explanation :
Explanation :
Let the numbers be 37a and 37b.
Then, 37a x 37b = 4107
ab = 3.
Now, coprimes 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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Q547. 

1)  40  2)  80 
3)  120  4)  200 
5)  None of these 
Answer : 40
Explanation :
Explanation :
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.
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Q548. 

1)  12  2)  16 
3)  24  4)  48 
5)  None of these 
Answer : 48
Explanation :
Explanation :
Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.
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Q549. 

1)  37years  2)  30years 
3)  47 years  4)  57 years. 
5)  None of these 
Answer : 47 years
Explanation :
Explanation :
Total age of 30 boys = 3016 = 480
After teacher's join, total age = 3117= 527
Teacher's age = 527 480 = 47 years.
Shortcut Method :
(311) + 16 = 47 years.
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Q550.  A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is: 
1)  145  2)  253 
3)  370  4)  352 
5)  None of these 
Answer : 253
Explanation : Let the middle digit be x.
Then, 2x = 10 or x = 5. So, the number is either 253 or 352.
Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit.
Hence, required number = 253.
Explanation : Let the middle digit be x.
Then, 2x = 10 or x = 5. So, the number is either 253 or 352.
Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit.
Hence, required number = 253.
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