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

TheNightKing · Answer

Bunuel

Can you help me with this question?

1. I got confused by what the table is. The "x" on the top left corner: I read it as x and not multiplication.

2. Even if I go past point 1, I am still not sure on how to approach this question.

sayan640 · Answer

Hey  TheNightKing  ,
Please refer to my explanation above. Please let me know if you have any doubt.
Also, please give me kudos if you find it helpful.

TheNightKing · Answer

Thank you Sir. Since you wrote each of the multiplications explicitly it became easier to see what's happening.

Rtmt · Answer

Hey sayan 
I am not able to understand the login behind the multiplication results explanations

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.

willnguyen2409 · Answer

still not sure about it. isn't statement 2 say c =f ==> f^2 = j

MBAB123 · Answer

Yes, that is correct. But, what if C = 0, then A could literally B any value and hence that statement is not sufficient.

We need statement 1 to make sure that C is not equal to 0 as it says that b*c=h and h ≠ 0, which implies that neither C nor B is 0.

Hope that helps!

Bambi2021 · Answer

Given:
a*c = f

(1) h is not 0.

c*b = h --> c can not be 0.

a can take different values. Not sufficient.

(2): c = f

a can be 0 if c and f are both 0:
0*0 = 0

a can be 1:
1*1 = 1
1*10 = 10

a can be negative if c and f are both 0:
-1*0 = 0

a can take different values. Not sufficient.

(1) + (2):

If c can not be 0, a can not be negative.
If c can not be 0, a can not be 0.

a can only be 1:

a*c = f, c = f -->

1*1 = 1
1*10 = 10

Crytiocanalyst · Answer

Statement 1 is clearly insufficient individually
Statement 2 :
ac=f from table gives a=1 ; however a=0 also satisfies the condition 
therefore insufficient 
Now staement 1 and 2 together 
bc=h ,=>b and c not equal to zero and bc = f , therefore f has to be non-zero 
hence a=1 suff 
Therefore IMO C

shrgmat · Answer

Great Qn; never get thrown off by the really hard looking problem. They’re never too difficult to solve. This is the evidence

Posted from my mobile device

Kimberly77 · Answer

Thanks  Basshead . Why is the need to test below two cases when c = 0, a=1 already? And how is a could be any value? Not sure what did I miss? Thanks for your time in advanced.

if c = 0, a = any value
if a = 1, c = any value

JDLaw · Answer

Lets take the statements directly,
1) h is non zero
and from table, 
cb=h
Therefore, c and b are non zero from 1.
This doesn't help find value of a.
2) c=f
and from table,
f=ac
before you go cancelling the common value c and f.  Please note that we can cancel it only if we know that c and f are non zero.
  and if we cannot cancel then this statement also doesn't help us get value of a.

Combining, we can say in the eqn. 2, c and f are non zero from enq. 1. So, we can cancel the common value of c and f from statement 2 inference.
and we get a=1.
This is a single answer. hence combined statement is the answer. Ans-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)

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards