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Question Stats:
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31%
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If a and b are integers, and 2a + b = 17, then 8a + b cannot equal which of the following?
A) -1
B) 33
C) 35
D) 65
E) 71
A) -1
B) 33
C) 35
D) 65
E) 71
alldaytestprep
Expert
Tutor
Joined: 08 May 2018
Last visit: 24 Apr 2023
Posts: 98
Affiliations: All Day Test Prep
Location: United States (IL)
Schools: Booth '20 (A)
GMAT 1: 770 Q51 V49
GRE 1: Q167 V167
GPA: 3.58
Expert reply
If a and b are integers, and 2a + b = 17, then 8a + b cannot equal which of the following?
A) -1
B) 33
C) 35
D) 65
E) 71
from 1st equation: b =17 - 2a
Plug into question: 8a + (17 - 2a) cannot equal which of the following -----> 6a + 17 cannot equal which of the following
Final rephrase: Which of the following cannot be represented as a multiple of 6 + 17
A) - 18 + 17 = -1 -----> -18 = multiple of 6
B) 16 + 17 = 33 -----> 16 = NOT a multiple of 6 -----------> B is our answer
C) 18 + 17 = 35 ----> 18 = multiple of 6
D) 48 + 17 = 65 ----> 48 = multiple of 6
E) 54 + 17 = 71 -----> 54 = multiple of 6
Answer: B
A) -1
B) 33
C) 35
D) 65
E) 71
from 1st equation: b =17 - 2a
Plug into question: 8a + (17 - 2a) cannot equal which of the following -----> 6a + 17 cannot equal which of the following
Final rephrase: Which of the following cannot be represented as a multiple of 6 + 17
A) - 18 + 17 = -1 -----> -18 = multiple of 6
B) 16 + 17 = 33 -----> 16 = NOT a multiple of 6 -----------> B is our answer
C) 18 + 17 = 35 ----> 18 = multiple of 6
D) 48 + 17 = 65 ----> 48 = multiple of 6
E) 54 + 17 = 71 -----> 54 = multiple of 6
Answer: B
General Discussion
JeffTargetTestPrep
Expert
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,973
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert reply
Posts: 2,973
CAMANISHPARMAR
We see that 8a + b is 6a more than 2a + b. So 8a + b = 17 + 6a. Since 6a is a multiple of 6, the difference between the answer choice (if it can be the value of 8a + b) and 17 must be a multiple of 6. The one that is not a multiple of 6 is the answer. Let’s analyze the choices.
A) -1 - 17 = -18 is a multiple of 6.
B) 33 - 17 = 16 is NOT a multiple of of 6.
(We see that B is the answer, but let’s check the other ones to make sure.),
C) 35 - 17 = 18 is a multiple of 6.
D) 65 - 17 = 48 is a multiple of 6.
E) 71 - 17 = 54 is a multiple of 6.
Answer: B
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Posts: 16
Multiply 2a + b = 17 by 4
You get 8a + 4b = 68
Let 8a + b = x
Subtract 2 from 1 to get
3b = 68 - x
On plugging in values from the option the only one that doesn't yield integer is 33
So option B
You get 8a + 4b = 68
Let 8a + b = x
Subtract 2 from 1 to get
3b = 68 - x
On plugging in values from the option the only one that doesn't yield integer is 33
So option B
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