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

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Attachment: 2018.OG.06.288.q.jpg [ 8.83 KiB | Viewed 15351 times ]
In the multiplication table above, each letter represents an integer. What is the value of c ?

(1) c=f

(2) h≠0
Target Test Prep Representative V
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Re: In the multiplication table above, each letter represents an integer.  [#permalink]

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AbdurRakib wrote:
Attachment:
2018.OG.06.288.q.jpg
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.

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##### General Discussion
Retired Moderator P
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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

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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 .

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

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3
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.

Intern  B
Joined: 03 Dec 2017
Posts: 13
Re: In the multiplication table above, each letter represents an integer.  [#permalink]

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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.
Intern  Joined: 04 May 2015
Posts: 4
Re: In the multiplication table above, each letter represents an integer.  [#permalink]

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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.

Intern  B
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Schools: Guanghua"21 (A)
GMAT 1: 700 Q49 V36 Re: In the multiplication table above, each letter represents an integer.  [#permalink]

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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?
Intern  B
Joined: 06 Sep 2018
Posts: 36
GMAT 1: 760 Q50 V44 GMAT 2: 740 Q48 V44 Re: In the multiplication table above, each letter represents an integer.  [#permalink]

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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?
Math Expert V
Joined: 02 Sep 2009
Posts: 59729
Re: In the multiplication table above, each letter represents an integer.  [#permalink]

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gmat800live wrote:
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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Joined: 11 Aug 2018
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Re: In the multiplication table above, each letter represents an integer.  [#permalink]

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gmat800live wrote:
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?

Gmat wording is too convoluted I think one has to get used to it.
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Re: In the multiplication table above, each letter represents an integer.  [#permalink]

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_________________ Re: In the multiplication table above, each letter represents an integer.   [#permalink] 20 Nov 2019, 06:15
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