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Consider a 7 digit Integer x=ABC78DE. If x is divisible by 8

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Consider a 7 digit Integer x=ABC78DE. If x is divisible by 8 [#permalink]

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New post 06 Nov 2016, 08:28
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Consider a 7 digit Integer x=ABC78DE. If x is divisible by 8, what is the value of two-digit integer DE?

(1) x is divisible by 5
(2) D is divisible by 8
[Reveal] Spoiler: OA

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Last edited by stonecold on 06 Nov 2016, 08:47, edited 2 times in total.
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Re: Consider a 7 digit Integer x=ABC78DE. If x is divisible by 8 [#permalink]

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stonecold wrote:
Consider a 7 digit Integer x=ABC78DE. If x is divisible by 8, what is the value of two-digit integer DE?

(1) x is divisible by 5
(2) D is divisible by 8


FROM STATEMENT - I ( NOT SUFFICIENT )

Since x is divisible by 5

E must be 0 or 5

However since x is divisible by 8 , E can not be 5 , so, E is 0

However from this statement we can not find the value of D from this statement....

FROM STATEMENT - II ( NOT SUFFICIENT )

Value of D must be 8 , thats the only digit divisible by 8

From this statement we can not find the value of E, since rule of divisibility of number 8 states that the last 3 digits , ie 8DE must be divisible by 8

FROM STATEMENT - I & II ( SUFFICIENT )

We know from statement I that E = 0 , further from statement II we know D is 8

So, DE = 80

Hence, BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked, answer will be (C)


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Consider a 7 digit Integer x=ABC78DE. If x is divisible by 8 [#permalink]

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New post 06 Nov 2016, 22:45
stonecold wrote:
Consider a 7 digit Integer x=ABC78DE. If x is divisible by 8, what is the value of two-digit integer DE?

(1) x is divisible by 5
(2) D is divisible by 8



x=ABC78DE and is divisible by 8. Value of DE=?

From statement 1
x is divisible by 5. we also know that x is divisible by 8
hence to be divisible by both 5 and 8 DE must be 40 or 80
no certain value is deduced hence insufficient.

From Statement 2
D is divisible by 8. Hence D can be 0 or 8.
But x=ABC78DE is divisible by 8.
8DE has to be divisible by 8.
88E or 80E has to be divisible by 8 hence E can have 2 values 8 or 0
hence insufficient.

Combining
we get DE=80
Hence C

Last edited by Vinayak Shenoy on 08 Nov 2016, 22:46, edited 1 time in total.

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Re: Consider a 7 digit Integer x=ABC78DE. If x is divisible by 8 [#permalink]

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New post 08 Nov 2016, 12:05
In statement 2, why is D can only be 8? 0 is also divisible by 8. So D should be 8 or 0.

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Re: Consider a 7 digit Integer x=ABC78DE. If x is divisible by 8 [#permalink]

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New post 08 Nov 2016, 22:45
adeelj80 wrote:
In statement 2, why is D can only be 8? 0 is also divisible by 8. So D should be 8 or 0.


Yes! You are right Adeelj80. D can be 0 or 8. When checking divisibility by 8 you have to check only last 3 numbers.
8DE can be of the form 88E or 80E as you pointed out.
Thanks for the correction :)

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Re: Consider a 7 digit Integer x=ABC78DE. If x is divisible by 8 [#permalink]

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New post 21 Dec 2017, 18:51
I do not think gmat will have amath question that has many unobvious information.
2 digit number DE => D cannot be 0. Not everybody can see that.

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Re: Consider a 7 digit Integer x=ABC78DE. If x is divisible by 8 [#permalink]

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New post 26 Dec 2017, 20:09
chesstitans wrote:
I do not think gmat will have amath question that has many unobvious information.
2 digit number DE => D cannot be 0. Not everybody can see that.

The Answer should be E. I think every one has missed one point. Let me explain.
Divisibility Rule of 8: Last three digits divisible by 8.,i.e, in this case 8DE should be divisible by 8.

Now coming to the possible values as per statement 1.
since, x is divisible by 5, Last digit is 0 or 5. Thus, 8D0 or 8D5.
Alone not sufficient.

Now coming to the possible values as per statement 2.
since, D is divisible by 8. Thus, D has only 2 values 0 or 8.
Alone not sufficient.

Combining I & II,
All possible cases for last three digits are, 800,880,805,885.
Now as per the question, x is divisible by 8, thus recall the rule mention in the begining.
Thus, eliminate 885 & 805. The cases left are 800 and 880 since both are divisible by 8.
Thus, two possible values of DE is 00 and 80.
Hence, E together not sufficient. [ Remember any number D is divisble by 0]

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Re: Consider a 7 digit Integer x=ABC78DE. If x is divisible by 8 [#permalink]

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New post 26 Dec 2017, 20:16
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Awanish01 wrote:
chesstitans wrote:
I do not think gmat will have amath question that has many unobvious information.
2 digit number DE => D cannot be 0. Not everybody can see that.

The Answer should be E. I think every one has missed one point. Let me explain.
Divisibility Rule of 8: Last three digits divisible by 8.,i.e, in this case 8DE should be divisible by 8.

Now coming to the possible values as per statement 1.
since, x is divisible by 5, Last digit is 0 or 5. Thus, 8D0 or 8D5.
Alone not sufficient.

Now coming to the possible values as per statement 2.
since, D is divisible by 8. Thus, D has only 2 values 0 or 8.
Alone not sufficient.

Combining I & II,
All possible cases for last three digits are, 800,880,805,885.
Now as per the question, x is divisible by 8, thus recall the rule mention in the begining.
Thus, eliminate 885 & 805. The cases left are 800 and 880 since both are divisible by 8.
Thus, two possible values of DE is 00 and 80.
Hence, E together not sufficient. [ Remember any number D is divisble by 0]


The point is that 00 is NOT a two-digit integer, it's a singe-digit integer 0.
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Re: Consider a 7 digit Integer x=ABC78DE. If x is divisible by 8 [#permalink]

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New post 27 Dec 2017, 21:02
stonecold wrote:
Consider a 7 digit Integer x=ABC78DE. If x is divisible by 8, what is the value of two-digit integer DE?

(1) x is divisible by 5
(2) D is divisible by 8



Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.


The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

We can modify the original condition and question as follows.

Since x is divisible by 8, 8DE is divisible by 8, which means 800 + 10D + E is divisible.
Thus both conditions togegher, they are sufficient.
E is 0 or 4 from the condition 1) and D = 8 from the condition 2)

Therefore, C is the answer.
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Re: Consider a 7 digit Integer x=ABC78DE. If x is divisible by 8   [#permalink] 27 Dec 2017, 21:02
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