Each entry in the multiplication table above is an integer that is eit

Question

https://gmatclub.com/forum/download/file.php?id=50482 Each entry in the multiplication table above is an integer that is either positive, negative, or zero. What is the value of a ? (1) h ≠ 0 (2) c = f DS95850.01 2019-09-22_0607.png

gvij2017 · Accepted Answer

h= b*c
h is not equal to zero so neither b nor c is zero. 
but this doesn't tell about a. 
not sufficient.

Statement-2 
c=f 
a*c= f 
this expression can hold if c=f=0
a can have any value. 
 and If C=F= any value, a is always 1. 
not sufficient

Statement 1+2
value of c is except zero. 
and for these value, a is always 1.

C is correct answer.

sayan640 · Answer

First, the significance of multiplication table needs to be understood.
This is like a 3*3 matrix and results in the following products ,
a^2 = d
a*b = e 
a*c = f
a*b = e
b^2 = g
b*c = h
c*a = f 
c*b = h 
c^2 = j

Now statement 1 says ,
h is not equal to 0.
That means neither b nor c equals zero as b*c = h;
But we cant tell anything about a.

Statement 2 says , c =f 
a*c = f
a*c = c
c*(a-1) = 0
Now a can be equal to 1 or c can be equal to 0 . 
So a can be equal to 1 or a may not be equal to 1 .
Not sufficient.

Together ,
c *(a-1) = 0
From statement h not equal to zero means c is not equal to zero.
If c is not equal to zero then (a-1) = 0 ( As we can divide the zero by c which is a non zero quantity )
Hence , a = 1
So option C is the answer.

Please give me KUDO s if you liked my explanation.
 GMATNinja   VeritasKarishma

exc4libur · Answer

any letter is an integer positive, negative or zero

(1) insufic
bc=h≠0, so (b,c,h) are not 0
no info about a or d

(2) insufic
c=f, ac=f, ac=c, ac=c
c=0, then, a=anything
a=1, then, c=anything

(1/2) sufic
c≠0, thus,
a=1, then, c=anything≠0

Ans (C)

Basshead · Answer

What is the value of a?

(1) h ≠ 0
b * c = h

This statement tells us that neither b nor c are zero. However, we can't determine the value of a. INSUFFICIENT.

(2) c = f

The chart tells us c * a = f

We can conclude a = 1 or c = 0
if c = 0, a = any value
if a = 1, c = any value

INSUFFICIENT.

(1&2) From statement 1 we know c ≠ 0. Therefore we can conclude a = 1. SUFFICIENT.

Answer is C.

willnguyen2409 · Answer

why C please?

the table also shows c * c = j --> f * f = j ; f # j => f # 0 ==> c #0 ==> B is sufficient.

MBAB123 · Answer

willnguyen2409 , that is now how this multiplication table works. Only the first operation that you have mentioned is correct. Sayan has explained the table perfectly in the following manner -

This is like a 3*3 matrix and results in the following products ,
a^2 = d
a*b = e
a*c = f
a*b = e
b^2 = g
b*c = h
c*a = f
c*b = h
c^2 = j

The above calculations are the only ones being shown by the table. Let me know if this doesn't help and you need more clarity on why the answer is C.

KarishmaB · Answer

Without considering any statements, we see that there are no constraints on the values of a, b and c. No where is the product shown to be the same as one of the multipliers. No two products are the same until and unless the same two numbers are multiplied together. Hence a, b, c could be anything.

(1) h ≠ 0

This tells us that neither b nor c is 0. No info about a. Not sufficient.

(2) c = f

We are shown that ca = f
If c = f, it means either a = 1 or c = f = 0 and a can be anything. Not sufficient.

Using both together, we see that c is not 0, hence a = 1. Sufficient.

Answer (C)

keshubhturakhia · Answer

Here how do we know that two terms can be the same but they can have different letters too?

Bunuel · Answer

If I understood you correctly, you’re asking whether different letters can represent the same number. The answer is yes, unless explicitly stated otherwise, different letters can represent the same number. This is also clear from the question itself, since the second statement directly gives c = f.

Each entry in the multiplication table above is an integer that is eit

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Each entry in the multiplication table above is an integer that is eit

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