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When 55 is divided by 3x the remainder is 2x. What is the value of x?

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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

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New post 17 Oct 2016, 15:11
The OA states => This problem is a good candidate for the "Pick Numbers / Play Devil's Advocate" strategy, as if you can come up with two different values of x, you can prove that a statement is not sufficient.

Yes but they did not mention that this will take eternity.

Bottom line => Solve by any method you like. => This Question is just plain too time consuming.
Maybe an out of bound question too
:)
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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

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New post 25 May 2020, 01:16
Hi,

I believe it needs to be mentioned that x is positive, since x can be -55 also. This is demonstrated as follows:

When 55 is divided by 3x the remainder is 2x. What is the value of x?

(1) x is an odd integer

(2) x is a 2-digit integer

from the prompt, we have the general form wherein 55 = 3x*y + 2x (y signifies the particular multiple we take of 3x)

simplifying this, we derive x = 55/(3y + 2)

Now as per statement 2, if y can only be positive, then certainly x can only be 11. However, y can also be negative, in which case when y=-1, x = -55.
To verify that x = -55 is a valid answer, we can plug the same in the first equation derived from the prompt:
55 = 3x*y + 2x
plugging in x = -55 and y = -1 in RHS, we get : 3(-55)(-1) + 2(-55)
165 - 110
55
Therefore, I believe that if B is to be the answer, it must be specified that x is positive, or some other constrained must be mentioned such that we do not consider negative multiples of the divisor, 3x.

Bunuel VeritasKarishma mikemcgarry

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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?  [#permalink]

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New post 28 May 2020, 01:11
sidship21 wrote:
Hi,

I believe it needs to be mentioned that x is positive, since x can be -55 also. This is demonstrated as follows:

When 55 is divided by 3x the remainder is 2x. What is the value of x?

(1) x is an odd integer

(2) x is a 2-digit integer

from the prompt, we have the general form wherein 55 = 3x*y + 2x (y signifies the particular multiple we take of 3x)

simplifying this, we derive x = 55/(3y + 2)

Now as per statement 2, if y can only be positive, then certainly x can only be 11. However, y can also be negative, in which case when y=-1, x = -55.
To verify that x = -55 is a valid answer, we can plug the same in the first equation derived from the prompt:
55 = 3x*y + 2x
plugging in x = -55 and y = -1 in RHS, we get : 3(-55)(-1) + 2(-55)
165 - 110
55
Therefore, I believe that if B is to be the answer, it must be specified that x is positive, or some other constrained must be mentioned such that we do not consider negative multiples of the divisor, 3x.

Bunuel VeritasKarishma mikemcgarry

Thanks



GMAT considers remainders to be positive only so x cannot be negative.
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Re: When 55 is divided by 3x the remainder is 2x. What is the value of x?   [#permalink] 28 May 2020, 01:11

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When 55 is divided by 3x the remainder is 2x. What is the value of x?

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