If a, b, and c are integers and a(b - c) is odd, which of the followin

Question

If a, b, and c are integers and a(b - c) is odd, which of the following must be odd?

A. b
B. c
C. ab
D. ab + c
E. abc

BrentGMATPrepNow · Accepted Answer

Another approach here is to  test some values  that satisfy the initial condition

If a(b - c) is odd, then it COULD be the case that  a = 1, b = 2 and c = 1 
Now let's plug these values into our answer choices...

A. b = 2
2 is NOT odd, so eliminate A

B. c = 1
1 is odd, so keep B

C. ab = (1)(2) = 2
2 is NOT odd, so eliminate C

D. ab + c = (1)(2) + 1 = 3
3 is odd, so keep D

E. abc = (1)(2)(1) = 2
2 is NOT odd, so eliminate E

At this point, we're left with answer choices B and D
So that's test another set of values

If a(b - c) is odd, then it COULD be the case that  a = 2, b = 1 and c = 1 
Now let's plug these values into the remaining answer choices...

B. c = 2
2 is NOT odd, so eliminate B

By the process of elimination, the correct answer must be D

Cheers,
Brent

CareerGeek · Answer

a(b - c) is odd
--> a = odd & b - c = odd

So, Possible combinations of (a, b, c) = (o, e, o) or (o, o, e)

A. b --> can be odd or even -->  No 
B. c --> can be odd or even -->  No 
C. ab = o*o or o*e -->  No 
D. ab + c = o*o + e = o or o*e + o = o --> Odd always -->  Yes 
E. abc = o*o*e = e or o*e*o = e -->  No

Option D

Jawad001 · Answer

Here Odd = o and Even =e
a………..b………..c……….a(b-c)
o………..o……….e……….o*(o-e) =o……..First case
o………..e……….o……….o*(e-o) = o…….Second Case

From the cases above, ab +c = o + e = o
 ab + c = e + o = o
Ans:D

sujoykrdatta · Answer

Question:  
If a, b, and c are integers and a(b - c) is odd, which of the following must be odd?
A. b
B. c
C. ab
D. ab + c
E. abc

Solution:

a(b - c) is odd
=> a is odd AND (b - c) is odd
=> a is odd AND b is even and c is odd ... (possibility 1)
OR a is odd AND b is odd and c is even ... (possibility 2)

Let us check the options: 
A) b : As discussed above, b could be even or odd - hence, incorrect
B) c : As discussed above, b could be even or odd - hence, incorrect
C) ab: As discussed above, b could be even or odd => hence, ab could be even or odd - hence, incorrect
D) ab + c: 
 According to Possibility (i): odd x even + odd = odd
 According to Possibility (ii): odd x odd + even = odd
 Hence, this option is correct
E) abc: It is clear that since b or c may be even or odd, abc could also be even or odd - hence, incorrect

Answer D

ScottTargetTestPrep · Answer

The only way to obtain an odd product is for both of the factors to be odd, since odd x odd = odd.

Since a(b - c) is odd, then a must be odd and (b - c) must be odd, which means b is odd when c is even, or vice versa. Thus, ab will be even when c is odd,  or  ab will be odd when c is even. In any case, ab + c is odd.

Answer: D

vasu1104 · Answer

a(b-c) = odd
 
when product of two integer is odd, both the integers must be odd.

so, a must be odd.

but for b-c, its not possible to have both odd.
but we know that b-c must be odd.
for that to happen, either of b or c must be odd and other must be even.

so c-1, a= odd, b= even, c= odd
c-2, a=odd, b=odd, c=even.

A not must be true.
B not must be true. can be even as well
C not always.
D perfect, either of case will always get odd.
E not always.

choice D

vasu1104 · Answer

a(b-c) = odd
 
when product of two integer is odd, both the integers must be odd.

so, a must be odd.

but for b-c, its not possible to have both odd.
but we know that b-c must be odd.
for that to happen, either of b or c must be odd and other must be even.

so c-1, a= odd, b= even, c= odd
c-2, a=odd, b=odd, c=even.

A not must be true.
B not must be true. can be even as well
C not always.
D perfect, either of case will always get odd.
E not always.

choice D

vasu1104 · Answer

a(b-c) = odd
 
when product of two integer is odd, both the integers must be odd.

so, a must be odd.

but for b-c, its not possible to have both odd.
but we know that b-c must be odd.
for that to happen, either of b or c must be odd and other must be even.

so c-1, a= odd, b= even, c= odd
c-2, a=odd, b=odd, c=even.

A not must be true.
B not must be true. can be even as well
C not always.
D perfect, either of case will always get odd.
E not always.

choice D

If a, b, and c are integers and a(b - c) is odd, which of the followin

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If a, b, and c are integers and a(b - c) is odd, which of the followin

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards