When x is divided by 2, the remainder is 1 and y is divided

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BTGmoderatorLU: Moderator; Posts: 2607; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Mon Aug 13, 2018 2:18 pm

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Source: GMAT Prep

When x is divided by 2, the remainder is 1 and y is divided by 8, the remainder is 2. Which of the following
could be the value of 2x + y? (x and y are integers)

A. 10
B. 11
C. 12
D. 13
E. 14

The OA is C.

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Source: Beat The GMAT — Problem Solving | Mon Aug 13, 2018 2:18 pm

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by [email protected] » Mon Aug 13, 2018 6:02 pm

Hi All,

We're told that X and Y are INTEGERS, when X is divided by 2, the remainder is 1 and when Y is divided by 8, the remainder is 2. We're asked which answer COULD be the value of 2X + Y. This question can be solved by TESTing VALUES.

Since X/2 has a remainder of 1, then X must be ODD: 1, 3, 5, 7, 9, 11, etc.
This means that 2X will be EVEN (but not every even number is possible): 2, 6, 10, 14, 18, 22.....

Since Y/8 has a remainder of 2, Y could be.... 2, 10, 18, 26, etc.

The answer choices are relatively small, so we should be looking at the smaller possibilities for 2X and Y. Two possibilities lead to the same correct answer:
IF.... 2X = 2 and Y = 10, then (2X + Y) = 12
IF.... 2X = 10 and Y = 2, then (2X + Y) = 12

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Aug 14, 2018 1:54 am

BTGmoderatorLU wrote: Source: GMAT Prep

When x is divided by 2, the remainder is 1 and y is divided by 8, the remainder is 2. Which of the following
could be the value of 2x + y? (x and y are integers)

A. 10
B. 11
C. 12
D. 13
E. 14

Algebraic approach:

When x is divided by 2, the remainder is 1.
In other words, x is a multiple of 2 plus 1:
x = 2a + 1.

When y is divided by 8, the remainder is 2.
In other words, y is a multiple of 8 plus 2:
y = 8b + 2.

Thus:
2x + y = 2(2a+1) + (8b + 2) = 4a + 2 + 8b + 2 = 4a + 8b + 4 = 4(a + 2b + 1).
The expression in blue indicates that the correct answer must be a MULTIPLE OF 4.

The correct answer is C.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Sat Aug 18, 2018 6:37 pm

BTGmoderatorLU wrote: Source: GMAT Prep

When x is divided by 2, the remainder is 1 and y is divided by 8, the remainder is 2. Which of the following
could be the value of 2x + y? (x and y are integers)

A. 10
B. 11
C. 12
D. 13
E. 14

We see that x could be 1, 3, 5, etc. and y could be 2, 10, 18, etc. We see that x is odd and y is even, so 2x + y is even. Since 2(1) + 10 = 12, we see that 2x + y could be 12.

Alternate Solution:

Since the remainder when x is divided by 2 is 1, x can be expressed as x = 2p + 1 for some integer p. Similarly, since the remainder when y is divided by 8 is 2, y can be expressed as y = 8q + 2 for some integer q. Then, multiplying the first equality by 2 and adding the result to the second equality, we obtain:

2x + y = 4p + 8q + 4

We notice that each of the terms 4p, 8q and 4 are divisible by 4, therefore 2x + y must be divisible by 4. The only answer choice that is divisible by 4 is 12.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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