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# The integers x and (x - 1) are not divisible by 4.

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The integers x and (x - 1) are not divisible by 4. [#permalink]  27 Jul 2017, 10:01
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38% (01:23) correct 61% (00:53) wrong based on 59 sessions
The integers x and (x - 1) are not divisible by 4.

 Quantity A Quantity B The value of the tenths digit of $$\frac{x}{4}$$ The value of the hundredths digit of $$\frac{x}{4}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The integers x and (x - 1) are not divisible by 4. [#permalink]  12 Aug 2017, 12:57
Hi,

Can you please explain the solution?
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Re: The integers x and (x - 1) are not divisible by 4. [#permalink]  13 Aug 2017, 01:57
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This is really a tough one. Whenever you see such question there is always a pattern underlined it.

now we do know that x -1 and x are consecutive positive integers.

if you pick a number you will see the pattern

1 and 2. follow that for x/4 x = 2 which means 2/4 = 1/2 = 0.50 and the tenth digit is 5 is always greater than the zero. 5 > 0 (zero is the hundredths digit)

2 and 3. follow that for x/4 you do have 3/4 = 0.75 and 7 > 5

5 and 6. follow that for x/4 you do have 6/4 = 3/2 = 1.50 and 5 > 0

and so on and so forth this pattern.

Therefore, the tenth digit is always greater than the hundredth digit

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Re: The integers x and (x - 1) are not divisible by 4. [#permalink]  11 Feb 2018, 01:40
Couldnt x be 1 and x-1 be 0

Isnt 0 also an integer?

Carcass wrote:
This is really a tough one. Whenever you see such question there is always a pattern underlined it.

now we do know that x -1 and x are consecutive positive integers.

if you pick a number you will see the pattern

1 and 2. follow that for x/4 x = 2 which means 2/4 = 1/2 = 0.50 and the tenth digit is 5 is always greater than the zero. 5 > 0 (zero is the hundredths digit)

2 and 3. follow that for x/4 you do have 3/4 = 0.75 and 7 > 5

5 and 6. follow that for x/4 you do have 6/4 = 3/2 = 1.50 and 5 > 0

and so on and so forth this pattern.

Therefore, the tenth digit is always greater than the hundredth digit

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Re: The integers x and (x - 1) are not divisible by 4. [#permalink]  12 Feb 2018, 03:15
Expert's post
No. Cannot be zero x.

Otherwise, the quantities were unuseful. if you consider x as zero (that is an integer) then in the quantities x/4 is impossible. x/0 is indefinite. And the question would fall apart.

Hope this helps
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Re: The integers x and (x - 1) are not divisible by 4. [#permalink]  13 Apr 2019, 23:40
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a number that is not divisible by 4 will give either 1,2,3 as remainder. Hence when the remainder is divided by 4, the decimals we get will end in 0.25, 0.50 or 0.75. since x and x-1 are consecutive integers. this rules out 1 as reminder when x is divided by 4. E.g if x is 5 then x-1 is 4 which is divisible by 4 but not allowed by the question. So the only possibilities are 2 and 3 as remainder which give us 0.50 or 0.75 as decimals. in these decimal remainder we see that tenths digit is greater than the hundredths digit. so A is greater than B
Re: The integers x and (x - 1) are not divisible by 4.   [#permalink] 13 Apr 2019, 23:40
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