Mathmetics

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

Q541.
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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Q542.
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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Q543.
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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Q544.
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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Q545.
 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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Q546.
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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Q547.
Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:
1) 40 2) 80
3) 120 4) 200
5)None of these
Answer : 40
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.
The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
1) 12 2) 16
3) 24 4) 48
5)None of these
Answer : 48
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.
The average age of 30 boys in a class is 16. If the teacher's age is included, the average increases by one. What is the teacher's age ?

1) 37years 2) 30years
3) 47 years 4) 57 years.
5)None of these
Answer : 47 years
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.
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