If a, b, and c are integers, what is the value of a?

Hi All,

This is a great 'concept' question, and it doesn't require much math to solve it.

We're told that A, B and C are all integers. We're asked for the value of A.

1) (A - 7)(B - 7)(C - 7) = 0

With this Fact, we know that AT LEAST one of the variables MUST equal 7, while the other two variables could be ANY integer. Thus, A could be 7, but it could also be any other integer.
Fact 1 is INSUFFICIENT

2) BC = 18

This Fact tells us NOTHING about the value of A.
Fact 2 is INSUFFICIENT

Combined, we know...
(A - 7)(B - 7)(C - 7) = 0
BC = 18

From the second Fact (AND that the variables are all INTEGERS), neither B nor C can equal 7. If either of those variables was 7, then the other variable would have to be 18/7, which is NOT an option). Since those 2 variables CANNOT be 7, the variable A MUST be 7 (to satisfy the first Fact).
Combined, SUFFICIENT.

Final Answer:

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

My Answer is also C. But slightly from a differnt understanding.

Clue 1 - either a or b or c can be zero. So we cannot say the value for a. INSUFF

Clue 2 - bc = 18 means possible values for B and C are 1,2,3,6,9,18. No way we can say the value for A. So Insufficient.

Now considering both the clues, since B and C 1,2,3,6,9,18, to satisfy Clue 1, a should be 7. With both the clues, we can find the value for A.

C

1) (a-7)(b-7)(c-7)=0 ; any of the integer a,b,c should be 7 ; but we cant say which one. INSUFF
2) bc=18 ; so bc Ne 0; doesn't give any clue!!

combine both, we know b, c ne 0, so a should be 7.

Thanks for the help but still not getting it. If bc ne 0 doesn't one of them have to = 0 leaving only A to equal 0?

from (2), if bc =18 --> both b and c can not be 7 as 18 does not have 7 as factor

from (1), which means that (b-7) and (c-7) are not equal to 0

which means that a-7 = 0 ---> a =7

Hence answer is (c)

(1) (a-7)(b-7)(c-7) = 0

3 variables, 1 equation = insufficient

(2) bc=18

2 variables, 1 equation = insufficient

Combined:

3 variables, 2 equations, and you could substitute bc and be left with a

Answer: C

If a, b, and c are integers, what is the value of a?

(1) (a - 7)(b - 7)(c - 7) = 0
(2) bc = 18

This is my understanding.
(1) a =7, b = 7, c= 7 ( a,b,c are integers NOT distinct integers)
So a or b or c does not have to be equal to 7.

(2) bc = 18 (a cannot be found from this equation)

Ans: A.

Hi nsarmah1,

You have to be careful about how you use the information that you've been given.

In Fact 1, we're told that (A - 7)(B - 7)(C - 7) = 0. That does NOT mean that all three variables equal 7; it means that AT LEAST ONE of the variables equals 7. If B=7, the A could be ANY value. As such, Fact 1 is insufficient on its own.

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

Hi EMPOWERgmatRichC VeritasKarishma Bunuel chetan2u GMATPrepNow

Is below approach correct to combine both statements:
Facts:
1. If product of bc is not zero, the none of b or c can be equal to 0.
2. A product of two no = 18 suggests that 7 is not a factor of 18
since we are given a, b c are integers.

From fact 2 , I can conclude that (a-7) MUST BE equal to 0 since b/c can not
be equal to 0 (fact -1). Is this correct, or seems too complicated?
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Yes, that's solid reasoning.
I would add to your second point that, if bc = 18, then neither b nor c can equal 7 .

Given: a, b, and c are integers

Asked: What is the value of a?

(1) (a - 7)(b - 7)(c - 7) = 0
means either a or b or c = 7
But it does not mean that a must be 7
NOT SUFFICIENT

(2) bc = 18
Value of (b,c) pairs = {(1,18),(2,9),(3,6),(6,3),(9,2),(18,1)}
NOT SUFFICIENT

Combining (1) & (2)
(1) (a - 7)(b - 7)(c - 7) = 0
means either a or b or c = 7
(2) bc = 18
Value of (b,c) pairs = {(1,18),(2,9),(3,6),(6,3),(9,2),(18,1)}
It means that b & c are NOT = 7
a = 7
SUFFICIENT

IMO C

Hi adkikani,

YES - that is exactly correct.

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

Question Stem Analysis:

We are told that a, b, and c are integers, and we need to determine the value of a. No other information is provided in the question stem.

Statement One Alone:

\(\Rightarrow\) (a - 7)(b - 7)(c - 7) = 0

Using this statement together with the zero product property, we can conclude that either a, or b, or c must be equal to 7. However, this is not sufficient to determine the value of a. If we let b = 7 or c = 7 (or both), a can be 0, 5, 10, -4, or 7. Since there are more than one possible values of a, statement one alone is not sufficient.

Eliminate answer choices A and D.

Statement Two Alone:

\(\Rightarrow\) bc = 18

Using this statement, we are able to conclude that both b and c must be factors of 18. However, since we have no information about a, this is not sufficient to determine a unique value for a. Statement two alone is not sufficient.

Eliminate answer choice B.

Statements One and Two Together:

Using statement one, we know at least one of a, b, or c must be equal to 7. Using statement two, we know both b and c must be factors of 18, which also means that neither b nor c can equal 7. These two facts together imply that a must be equal to 7. Statements one and two together are sufficient.

Answer: C
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