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If x and y are three-digit positive integers whose digits ar

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If x and y are three-digit positive integers whose digits ar  [#permalink]

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New post 29 Jan 2019, 04:42
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Difficulty:

  75% (hard)

Question Stats:

49% (02:03) correct 51% (01:55) wrong based on 54 sessions

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If x and y are three-digit positive integers whose digits are the same but in reverse order, which of the following could not be the difference between x and y?

A) 0
B) 99
C) 198
D) 693
E) 891

Posted from my mobile device

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Re: If x and y are three-digit positive integers whose digits ar  [#permalink]

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New post 29 Jan 2019, 04:49
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rashedBhai wrote:
If x and y are three-digit positive integers whose digits are the same but in reverse order, which of the following could not be the difference between x and y?

A) 0
B) 99
C) 198
D) 693
E) 891

Posted from my mobile device


Let, x = abc = 100a + 10b + c
then, y = cba = 100c + 10b + a

x - y = 99 (a-c)

i.e. The result must be divisible by 99 and the quotient must be less than 9 because a-c can NOT be 9 or above as they are single non zero digits

891 = 99*9 hence this can NOT be the difference of x and y

Answer: Option E
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Re: If x and y are three-digit positive integers whose digits ar  [#permalink]

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New post 29 Jan 2019, 05:10
rashedBhai wrote:
If x and y are three-digit positive integers whose digits are the same but in reverse order, which of the following could not be the difference between x and y?

A) 0
B) 99
C) 198
D) 693
E) 891

Posted from my mobile device


If x and y are three-digit positive integers whose digits are the same but in reverse order

This will mean x = 100a + 10 b + c , y = 100c + 10 b + a

x - y = 100a +10b + c - 100c - 10b -a
= 99(a-c)

Now only case which cannot be possible will be E

Since 99 * 9 = 891, the difference between a-c can never be 9.

E
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Re: If x and y are three-digit positive integers whose digits ar  [#permalink]

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New post 29 Jan 2019, 05:26
rashedBhai wrote:
If x and y are three-digit positive integers whose digits are the same but in reverse order, which of the following could not be the difference between x and y?

A) 0
B) 99
C) 198
D) 693
E) 891

Posted from my mobile device



x= 100a+10b+c
y=100c+10b+c
x-y= 99(a-c)

answer would be the one which is factor of 99 and the difference of ( a-c) is any no <9 ; because a-c are both single digits and their difference would always be<9
so IMO E is odd option out..
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Re: If x and y are three-digit positive integers whose digits ar   [#permalink] 29 Jan 2019, 05:26
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