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11 Jan 2014, 06:19
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
59% (02:37) correct
41%
(02:18)
wrong
based on 250
sessions
History
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Not Attempted Yet
If X and Y are single-digit positive integers, is X + Y a multiple of 6?
(1) X + 4Y is an even integer.
(2) If Y and X were combined into a two-digit number, YX, with Y as the tens digit and X as the units digit, then YX would be divisible by 3.
OE
Hi, I found that solving this question takes time. I want to know if we have faster solution, please.
(1) X + 4Y is an even integer.
(2) If Y and X were combined into a two-digit number, YX, with Y as the tens digit and X as the units digit, then YX would be divisible by 3.
OE
Multiple of 6 by 2 single-digits = {6, 12, 18}
For Sum of 6 = (1 + 5), (2 + 4), or (3 + 3).
For Sum of 12 = (3 + 9), (4 + 8), (5 + 7), or (6 + 6).
For Sum of 18 = (9 + 9).
(1): (X + 4Y) = even → As 4Y = even → X = even
But, no restrictions on Y
Insufficient.
If X = 2, Y = 4, (X+4Y) = (2 + 4x4) = 10 is even. And (X + Y) = 6. Yes.
If X = 2, Y = 1, (X+4Y) = (2 + 4x1) = 6 is even. But (X + Y) = 3. No.
(2): A number is divisible by 3 if sum of its digits is multiple of 3 → (X + Y) =a multiple of 3
But, not necessarily a multiple of 6
Insufficient
if X = 2, Y = 4, YX = 42, divisible by 3. And (X + Y) = 6. Yes
if X = 2, Y = 1, XY = 12, divisible by 3. But (X + Y) = 3. No
Combined: (1) gives that (X + Y) is a multiple of 3, and (2) gives that X is even.
If X = 2, Y = 1, (X + Y) = 3, not a multiple of 6
If X = 2, Y = 4, (X + Y) = 6, a multiple of 6
Insufficient.
For Sum of 6 = (1 + 5), (2 + 4), or (3 + 3).
For Sum of 12 = (3 + 9), (4 + 8), (5 + 7), or (6 + 6).
For Sum of 18 = (9 + 9).
(1): (X + 4Y) = even → As 4Y = even → X = even
But, no restrictions on Y
Insufficient.
If X = 2, Y = 4, (X+4Y) = (2 + 4x4) = 10 is even. And (X + Y) = 6. Yes.
If X = 2, Y = 1, (X+4Y) = (2 + 4x1) = 6 is even. But (X + Y) = 3. No.
(2): A number is divisible by 3 if sum of its digits is multiple of 3 → (X + Y) =a multiple of 3
But, not necessarily a multiple of 6
Insufficient
if X = 2, Y = 4, YX = 42, divisible by 3. And (X + Y) = 6. Yes
if X = 2, Y = 1, XY = 12, divisible by 3. But (X + Y) = 3. No
Combined: (1) gives that (X + Y) is a multiple of 3, and (2) gives that X is even.
If X = 2, Y = 1, (X + Y) = 3, not a multiple of 6
If X = 2, Y = 4, (X + Y) = 6, a multiple of 6
Insufficient.
Hi, I found that solving this question takes time. I want to know if we have faster solution, please.
11 Jan 2014, 06:28
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goodyear2013
If X and Y are single-digit positive integers, is X + Y a multiple of 6?
(1) X + 4Y is an even integer --> this implies that x is an even integer. If x=2 and y=4, then the answer is YES but if x=2 and y=1, then the answer is NO. Not sufficient.
(2) If Y and X were combined into a two-digit number, YX, with Y as the tens digit and X as the units digit, then YX would be divisible by 3 --> this imples that x+y is a multiple of 3. Consider the same examples as for (1). Not sufficient.
(1)+(2) Bot examples are valid: x=2 and y=4, then the answer is YES but if x=2 and y=1, then the answer is NO. Not sufficient.
Answer: E.
28 Aug 2025, 07:37
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
