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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]

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New post 24 Mar 2018, 06:20
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.
Re: In the multiplication table above, each letter represents an integer.   [#permalink] 24 Mar 2018, 06:20
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In the multiplication table above, each letter represents an integer.

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