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

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In the multiplication table above, each letter represents an integer. [#permalink]

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

(1) c=f

(2) h≠0
[Reveal] Spoiler: OA

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Re: In the multiplication table above, each letter represents an integer. [#permalink]

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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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Re: In the multiplication table above, each letter represents an integer. [#permalink]

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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
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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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Re: In the multiplication table above, each letter represents an integer. [#permalink]

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

(1) c=f

(2) h≠0


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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Re: In the multiplication table above, each letter represents an integer.   [#permalink] 17 Nov 2017, 11:33
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