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

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Senior PS Moderator
Joined: 26 Feb 2016
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Two consecutive positive integers are divided by 25. What is the sum  [#permalink]

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01 Oct 2018, 06:38
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Difficulty:

95% (hard)

Question Stats:

24% (02:14) correct 76% (02:12) wrong based on 64 sessions

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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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01 Oct 2018, 08:14
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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

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

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17 Jan 2019, 09:16
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

integer would be divisible by 25 , when last two digits are 00,50,75
#1
last two digits sum is 49
we can say
x+x+1 = 49
x = 24
so
ab24 and ab25 could be two no ; remainder would be 24 ; sufficient
#2:
sum of remainders is even
for a no to be divisible by 25 the last digits have to be 00,24,75 so in the case to get even remainder the last two digits have to be both even 00, 24
sufficient

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

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17 Jan 2019, 09:38
In my opinion it is D
Re: Two consecutive positive integers are divided by 25. What is the sum   [#permalink] 17 Jan 2019, 09:38
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