Q:

(51 + 52 + 53 + .........+100) is equal to

Answer

51 + 52 + 53 + ...........+ 100


= (1 + 2 + 3 + .... + 100) - (! + 2 + 3 + ...... + 50)


=


=  (5050 - 1275) = 3775

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36 5977
Q:

What least number must be subtracted from 13601, so that the remainder is divisible by 87 ?

A) 23 B) 31
C) 29 D) 37
 
Answer & Explanation Answer: C) 29

Explanation:

87)13601(156
       87
       -----
       490
       435
        -----
        551
        522
         -----
         29
         -----
Required number is 29.

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29 5649
Q:

A number when divided by 296 leaves 75 as remainder.When the same number is divided by 37,the remainder will be:

A) 1 B) 3
C) 5 D) 2
 
Answer & Explanation Answer: A) 1

Explanation:

Let the Number be Y.

Then  Y = 296 q + 75

= (37 x 8)q +( 37 x 2) + 1

= 37 (8q + 2) + 1

Thus, when the number is divided by 37, the remainder is 1

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18 5402
Q:

The sum of all two digit numbers divisible by 5 is

A) 945 B) 678
C) 439 D) 568
 
Answer & Explanation Answer: A) 945

Explanation:

Required numbers are 10,15,20,25,...,95
This is an A.P. in which a=10,d=5 and l=95.
Let the number of terms in it be n.Then t=95
So a+(n-1)d=95.
10+(n-1)*5=95,then n=18.
Required sum=n/2(a+l)=18/2(10+95)=945.

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7 3837
Q:

The difference between a positive proper fraction and its reciprocal is 9 / 20. Then the fraction is :

A) 3/5 B) 3/10
C) 4/5 D) 5/4
 
Answer & Explanation Answer: C) 4/5

Explanation:

Let the required fraction be x. Then, (1 / x )- x = 9/20
1 - x^(2) / x = 9 / 20  =>  20 - 20 * x^(2) = 9 * x.
20 * x^(2) + 9 *x - 20 = 0.
=> (4 * x + 5) (5 * x - 4) = 0.
=> x = 4 / 5.

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6 3356