36.
The product of the L.C.M. and H.C.F. of two numbers is 24. The difference of two numbers is 2. Find the numbers.
• A.
2 and 4
• C.
8 and 6
• B.
6 and 4
• D.
8 and 10
• Report
Explanation :

Let the numbers be x and (x + 2).

 Then, x(x + 2) = 24 x2 + 2x - 24 = 0

 (x - 4) (x + 6) = 0

 x = 4

So, the numbers are 4 and 6

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37.
Let the least number of six digits, which when divided by 4, 6, 10 and 15, leaves in each case the same remainder of 2, be N. The sum of the digits in N is:
• A.
3
• C.
5
• B.
4
• D.
6
• Report
Explanation :

Least number of 6 digits is 100000.

L.C.M. of 4, 6, 10 and 15 = 60.

On dividing 100000 by 60, the remainder obtained is 40.

 Least number of 6 digits divisible by 4, 6, 10 and 15 = 100000 + (60 � 40) = 100020.

 N = (100020 + 2) = 100022. Sum of digits in N = (1 + 2 + 2) = 5

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38.
 1095 1168
when expressed in simplest form is:
•  A. 13 16
•  C. 17 26
•  B. 15 16
•  D. 25 26
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Explanation :

1095 ) 1168 (  1
1095
73 )  1095  (15
73

 365

 365

x

So, H.C.F. of 1095 and 1168 = 73.

1095 = 1095 + 73 = 15
1168 1168 + 73 16

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39.
The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:
• A.
15 cm
• C.
35 cm
• B.
25 cm
• D.
42 cm
• Report
Explanation :
 Required length = H.C.F. of �700 cm, 385 cm and 1295 cm = 35 cm
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40.
The least number which when increased by 5 is divisible by each one of 24, 32, 36 and 54, is
• A.
427
• C.
869
• B.
859
• D.
4320