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.
When x is divided by 2, the remainder is 1 and y is divided
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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
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
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Algebraic approach: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
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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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.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
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
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