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If B and A are consecutive integers and A + B + X = 15, then which of 12 Sep 2019, 23:24
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D
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78% (01:08) correct 22% (01:24) wrong based on 83 sessions

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If B and A are consecutive integers and A + B + X = 15, then which of the following must be true about X?

A. X is a multiple of 5
B. X is a multiple of 3
C. X is positive.
D. X is even.
E. X is odd.
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D
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If B and A are consecutive integers and A + B + X = 15, then which of 12 Sep 2019, 23:29
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Bunuel
If B and A are consecutive integers and A + B + X = 15, then which of the following must be true about X?

A. X is a multiple of 5
B. X is a multiple of 3
C. X is positive.
D. X is even.
E. X is odd.
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A + B + X = 15

A + A + 1 + X = 15

2A + 1 + x = 15

2A + X = 14 ( Even)

2A = EVEN

X = EVEN

D is the correct answer.
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If B and A are consecutive integers and A + B + X = 15, then which of Updated on: 13 Sep 2019, 12:09
Originally posted by Archit3110 on 13 Sep 2019, 03:04.
Last edited by Archit3110 on 13 Sep 2019, 12:09, edited 1 time in total.
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Bunuel
If B and A are consecutive integers and A + B + X = 15, then which of the following must be true about X?

A. X is a multiple of 5
B. X is a multiple of 3
C. X is positive.
D. X is even.
E. X is odd.
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given
a+1+a+X=15
2a+x=14
2a shall be even and 14-even ; even
so X has to be even integer
IMO D
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If B and A are consecutive integers and A + B + X = 15, then which of 13 Sep 2019, 04:25
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If B and A are consecutive integers and A + B + X = 15, then which of the following must be true about X?

X=15-(A+B)=15-(A+A+1)=14-2A

A. X is a multiple of 5 ... If A has units digit 2 or 7, yes, otherwise NO
X=14-2A..... X=14-2*2 or X=14-2*27...YES ... But X=14-2*2...NO

B. X is a multiple of 3 ... If A leaves a remainder of 1 when divided by 3.. yes, otherwise NO
X=14-2A..... X=14-2*4=6 or X=14-2*7=0...YES ... But X=14-2*2...NO

C. X is positive.... If A<7.. yes, otherwise NO
X=14-2A..... X=14-2*4=6 YES.... X=14-2*7=0...YES .....NO

D. X is even.Yes always
X=14-2A=2(7-A)S .....NO

E. X is odd.
Never, as C is even

D
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If B and A are consecutive integers and A + B + X = 15, then which of 13 Sep 2019, 12:01
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Bunuel
If B and A are consecutive integers and A + B + X = 15, then which of the following must be true about X?

A. X is a multiple of 5
B. X is a multiple of 3
C. X is positive.
D. X is even.
E. X is odd.
Show more

Given: B and A are consecutive integers and A + B + X = 15

Asked: Which of the following must be true about X?

B = A+1
A+B+X=15
2A+1+X=15
2A +X = 14
X = 14-2A
X = even since 14 and 2A are even

IMO D
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If B and A are consecutive integers and A + B + X = 15, then which of 13 Sep 2019, 12:03
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Archit3110
Bunuel
If B and A are consecutive integers and A + B + X = 15, then which of the following must be true about X?

A. X is a multiple of 5
B. X is a multiple of 3
C. X is positive.
D. X is even.
E. X is odd.

given
a+1+a+X=15
2a+x=14
2a shall be even and 15-even ; even
so X has to be even integer
IMO D
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Archit3110

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If B and A are consecutive integers and A + B + X = 15, then which of 13 Sep 2019, 12:10
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Kinshook
edited thanks

Kinshook
Archit3110
Bunuel
If B and A are consecutive integers and A + B + X = 15, then which of the following must be true about X?

A. X is a multiple of 5
B. X is a multiple of 3
C. X is positive.
D. X is even.
E. X is odd.

given
a+1+a+X=15
2a+x=14
2a shall be even and 15-even ; even
so X has to be even integer
IMO D

Archit3110

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If B and A are consecutive integers and A + B + X = 15, then which of 13 Sep 2019, 13:37
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Bunuel
If B and A are consecutive integers and A + B + X = 15, then which of the following must be true about X?

A. X is a multiple of 5
B. X is a multiple of 3
C. X is positive.
D. X is even.
E. X is odd.
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It says "which of the following," so this looks like a good problem to test cases on. The answer choices deal with evens, odds, and multiples, so we should definitely choose some even and some odd numbers. But, let's keep the numbers easy as well.

Case 1: A = 0, B = 1. Then, X = 15 - A - B = 15 - 1 = 14.

14 isn't a multiple of 5. Eliminate A.

14 isn't a multiple of 3. Eliminate B.

14 is positive. Keep C.

14 is even. Keep D.

14 isn't odd. Eliminate E.

Now, we have one answer that says "positive", and one that says "even." I'm going to try to eliminate the "positive" one by seeing if I can make X a negative number.

Case 2: When would X be a negative number? That would happen if A + B was large, so X had to be negative in order to reduce the sum back down to just 15.

So, if A = 10, B = 11, then x = 15 - 10 - 11 = -6.

X can be negative, so we can eliminate C. The correct answer is D.
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