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# Arithmetic Aptitude :: Numbers

Home > Arithmetic Aptitude > Numbers > General Questions

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1. When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?

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Explanation:

x = 13p + 11 and x = 17q + 9

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2. Which one of the following can't be the square of natural number ?

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Explanation:

The square of a natural number nerver ends in 2.

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3. 287 x 287 + 269 x 269 - 2 x 287 x 269 = ?

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Explanation:

Given Exp. = a2 + b2 - 2ab, where a = 287 and b = 269
= (a - b)2 = (287 - 269)2
= (182)
= 324

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4. The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

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Explanation:

Let the ten's digit be x and unit's digit be y.
Then, (10x + y) - (10y + x) = 36
=> 9(x - y) = 36

=> x - y = 4.

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ShortCut

5. A number when divided successively by 4, 5, and 6, leaves remainders 2, 3 and 4 respectively. The least such number is:

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Explanation:

58 is the answer because 58/4=2, 58/6=4 and 58/5=3.the least number is 58.

ShortCut By :: VIKAS KUMAR SINGH

Solution: The easiest way is to go by option verification.

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6. A number, when divided by 296, gives 75 as the remainder. If the same number is divided by 37 then the remainder will be

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Explanation:

If the first divisor is a multiple of second divisor, the remainder obtained by dividing the same number by second divisor = remainder obtained by dividing the first remainder by the second divisor.
Here, 296/37 = 8
So required remainder = Remainder obtained by dividing 75 by 37 = 1

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7. The sum and product of two numbers are 12 and 35 respectively. The sum of their reciprocals will be

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Explanation:

x+y = 12............(1)
xy = 35 ............(2)

so (x+y)/xy = 1/y+1/x = 12/35

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8. The sum of all the digits of the numbers from 1 to 100 is:

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Explanation:

Sum of unit digits of numbers from 1 to 99.
= 10 (1 + 2 + 3 + ..... + 9)
= 10*(9*l0/2)=450
= [1+2+3+....+n=n(n+l)/2]

Sum of ten's digits of numbers from 1 to 99
= 10 (1 + 2 + 3 + ..... 9) = 450
Sum of digits of 100 = 1
Required sum = 450 + 450 + 1 = 901

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9. Two numbers are such that their difference, their sum and their product arc in the ratio of 1:7:24. The product of the numbers is:

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Explanation:

(x-y) : (x+y) : xy= 1:7:24 = 2:14:48
so Number = 8 and 6

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10. B is taller than j and 3 pillers. P is shorter than B and 2 pillers. is j shorter/taller than P?

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