In the multiplication table above, each letter represents an integer.

We need to determine the value of c. Following our table, we have:

a x c = f

b x c = h

and

c^2 = j

Statement One Alone:

c = f

Since c = f, we have:

a x c = c

ac - c = 0

c(a - 1) = 0

c = 0 or a = 1

We see that either c = 0 or a = 1 (if c ≠ 0). Since we don’t know whether c is 0, we cannot determine the value of c. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

h ≠ 0

Since h is not zero, neither b nor c is zero. However, we still can’t determine the value of c. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statement two, we know that c ≠ 0, and thus from statement one, a = 1. However, c can be any nonzero number, so we still cannot determine a value for c.

Answer: E
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We can see that a*c = f and b*c = h

Statement 1. c=f, This means a*c = c.
So either a=1, and then c could take any value
OR c=0, then a could take any value. We cant say anything surely about c.

Statement 2. h ≠ 0. So b*c ≠ 0
This means neither of b or c can be 0, but we cant say anything surely about c.

Combining the two statements: a*c = c, where c ≠ 0
This means definitely a = 1, but c could be any integer except 0. Insufficient.

Hence E answer

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(1) c=f

This will not give us a value (a number) for c ===> NOT SUFFICIENT

(2) h≠0

This will still not help us to get the value of c ===> NOT SUFFICIENT

Lets combine (1) & (2) - we will still not be able to determine the value of c

Hence, Answer is E
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1) c=f
a)either a = 1 and c is any integer
b) c and f are both zeros .

We are not able to figure out the exact value of c .

2) h≠0
this shows that c,b≠0 . c could be any positive integer .

Taking together 1 and 2
this negates the case a . c can still be any integer except 0 .

Answer is E

The official explanation to this question is the following: But I still don't get it :-/


Arithmetic Properties of numbers

Given that c = f, the examples below, in which a = b = 1, show that the value of c could be 1 and the value of c could be 2; NOT sufficient.



Given that h ≠ 0, the examples in (1) show that the value of c could be 1 and the value of c could be 2; NOT sufficient.
Taking (1) and (2) together is of no more help than either (1) or (2) taken separately because the same examples used to show that (1) is not sufficient also show that (2) is not sufficient.

Both statements together are still not sufficient.

I see a problem in this question. In the multiplication table it is stated that:
a*a= d hence "a" cannot equal 1! other wise a*a would = a. so based on my observation I chose (A). because if a doesn't equal 1 then c=0.

for whom got an explanation please answer

there're 8 unknowns and 7 equations:
a^2=d
ab=e
af=c
b^2=g
bc=h
c^2=j
c=f
hence we cannot resolve c in this case.
does my logic make sense?

Hi, when the question says "each letter represents an integer" is it implied that each letter represents a different integer? Could c and b be the same integer for instance? It it doesn't specify "unique integer" then how can I assume it means that?

Unless it is explicitly stated otherwise, different variables CAN represent the same number.
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Gmat wording is too convoluted I think one has to get used to it.

From statement (1),

Can't we imply that C does not equal zero?

If c=0=f, then c^2 should equal to f. But that's not the case, as c^2 = j.

Similarly, c x b should equal to f. But that's not the case, as c x b = h

Therefore, there is no way for c to equal zero. This statement tells us that A must be = 1

Is my reasoning flawed?

In the multiplication table above, each letter represents an integer. What is the value of c ?

(1) c=f
We know c = f, but f can be any number.

(2) h≠0
does nothing to tell us about the value of C.

I don't think you have to do any calculations here. The question is specifically asking for the value of C, and none of the 2 statements provided gives you any values. So the answer is E.

S1: Using the table, this can be rewritten as ac=c. c could equal 0 if a is not equal to 1, or any real number if a is equal to 1. NOT SUFFICIENT.

S2: This can be rewritten as cb =/= 0 This tell us that neither b nor c is equal to 0, but nothing else. NOT SUFFICIENT.

S1+S2: Using S2, we can rule out 0 as a solution for c. This means a=1, and thus c could equal any real number. NOT SUFFICIENT - the correct answer is E.

The multiplication table says ac = f, ab = e and so on.

1) Says ac=c
If we take a = 0, then c will be 0, but if
a =1, C could be 1, 2, 3 ... any integer. So insufficient.

2) h not equal to 0, it mean bc ≠0, No information about c. Insufficient.

Using 1) and (2) C ≠ 0 but still c could be 1,2,3 as ac = c ; No unique value for C

Ans is E.
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silly doubt - doesnt the question imply the digits have to be different?

a^2 =d should then rule out a=1, and therefore 1 should definitely help us find C (C=0) ?

Unless it is explicitly stated otherwise, different variables CAN represent the same number.
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Answer: Option E

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Great explanation ScottTargetTestPrep. In Statement 1, calculation already show c = 0 or a = 1. Therefore wondering why we can't take c = 0 here and will need to assume that when c ≠ 0? Thanks.