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Two consecutive positive integers are divided by 25. What is the sum

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Two consecutive positive integers are divided by 25. What is the sum  [#permalink]

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New post 01 Oct 2018, 05:38
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Two consecutive positive integers are divided by 25. What is the sum of the remainders obtained?

A. The sum of the digits at the last two places of the consecutive number is 49
B. The sum of the remainders obtained is even

Source: Experts Global

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Re: Two consecutive positive integers are divided by 25. What is the sum  [#permalink]

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New post 01 Oct 2018, 07:14
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pushpitkc wrote:
Two consecutive positive integers are divided by 25. What is the sum of the remainders obtained?

A. The sum of the digits at the last two places of the consecutive number is 49
B. The sum of the remainders obtained is even

Source: Experts Global



Let the numbers be x and x+1...

1) The sum of the digits at the last two places of the consecutive number is 49
Any number divisible by 25 will have 00,25,50 or 75 as last two digits..
If the last two numbers are combined equal to 49, the remaining der is 49-25=24
Otherwise both consecutive means x+x+1=49 means last two digits are xy24 and xy25
Remainder is 24
Sufficient

2). The sum of the remainders obtained is even
Consecutive integers means one even and one odd and therefore remainder too will be one odd and one even so combined remainder is odd+even=ODD..
Only case when it is even is when it is even and 0 so 24 and 0
Thus remainder is 24
Sufficient

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Two consecutive positive integers are divided by 25. What is the sum &nbs [#permalink] 01 Oct 2018, 07:14
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Two consecutive positive integers are divided by 25. What is the sum

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