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# If d and e are positive integers, is d a multiple of 9?

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If d and e are positive integers, is d a multiple of 9? [#permalink]
BrentGMATPrepNow when we look at (2) or any statement like statement (2) do we need to find a few values to get a Yes and No situation OR could we simply see that since we have d = 5e + 2 i.e. since we have two variables and one constant we WILL get different values?

I know that on the GMAT we can have an equation with 2 variables that can be sufficient BUT in such questions we are given restrictions that help us get one definite answer. But in this question we do not have any restriction about d or e. So could we just eliminate (2) without analyzing it much?
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Re: If d and e are positive integers, is d a multiple of 9? [#permalink]
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BrentGMATPrepNow when we look at (2) or any statement like statement (2) do we need to find a few values to get a Yes and No situation OR could we simply see that since we have d = 5e + 2 i.e. since we have two variables and one constant we WILL get different values?

I know that on the GMAT we can have an equation with 2 variables that can be sufficient BUT in such questions we are given restrictions that help us get one definite answer. But in this question we do not have any restriction about d or e. So could we just eliminate (2) without analyzing it much?

It's difficult to derive a clear-cut rule for when you need to actually find values that show a statement is not sufficient.

For example, if statement 2 were something like d - 27 = 18e, then statement 2 would be sufficient.
Likewise, if statement 2 were something like d - 26 = 18e, then statement 2 would also be sufficient.
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Re: If d and e are positive integers, is d a multiple of 9? [#permalink]
Asked: If d and e are positive integers, is d a multiple of 9?

(1) 5e - 7 is a multiple of 9.
NOT SUFFICIENT

(2) d - 2 = 5e
d = 5e + 2
If d=27; d is a multiple of 9
But if d=22; d is NOT a multiple of 9.
NOT SUFFICIENT

(1) + (2)
(1) 5e - 7 is a multiple of 9.
(2) d - 2 = 5e
d = 5e + 2 = (5e-7) + 9 = 9k + 9 ; d is a multiple of 9
SUFFICIENT

IMO C
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Re: If d and e are positive integers, is d a multiple of 9? [#permalink]
S1 doesnt give us any information about d, but for the sake of it lets workout some values for what e can be

multiples of 9 are 9,18,27, 36, 54 63, 72, 81, 90 etc

if e= 5 , then d is a multiple of 9 because 5*5 - 7 = 18 which is a multiple of 9

if e = 14 then 5*14 = 70 and 70-7 = 63 which is a multiple of 9 therefore e can also be 14

S2 alone tells us that d= 5e+ 2

this is also clearly not sufficient on its own.

S1 + S2 plug in the values for e we found in S1 into S2 and see if the resulting value is a multiple of 9

5*5 + 2 = 27 --> multiple of 9
5*14 + 2 = 72 --> multiple of 9

We can then conclude the answer is C using both statements as whatever value we get for d is a multiple of 9

note that d can be 27 or 72 but either way it is a multiple of 9.
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Re: If d and e are positive integers, is d a multiple of 9? [#permalink]
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Re: If d and e are positive integers, is d a multiple of 9? [#permalink]
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