If y is a positive integer, what is

Question

If y is a positive integer, what is the value of y?

(1) \(y^3 = y^{1/3}\)
(2) \(ay = a\), and \(a < 1\)

Answer Choices

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B.Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Thanks,
Saquib
Quant Expert
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Show Answer

Official Answer

A

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varundixitmro2512 · Answer

IMO E

from 1 y can be 0 ,-1, 1 
from 2 a can be 0 or y can be 1

combining both 
a can be 0 and y can have any value
or y=1

so E

waiting for OA

VachePBH · Answer

It is mentioned that y is a positive integer, so I guess it's D

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jy295 · Answer

From A) The answer could be 1 , 0, or -1. However, the question prompt dictates that y must be positive, eliminating -1 and 0. A is sufficient.

From B) If a<1, a could be zero, in which case y could be any positive integer. If a does not equal 0, then y = 1. There are multiple solutions, Not Sufficient.

EgmatQuantExpert · Answer

Official Solution

Steps 1 & 2: Understand Question and Draw Inferences

Given:

To find:

• Value of y
Step 3: Analyze Statement 1 independently

• \(y^3 = y^{1/3}\)
To get rid of the cube root on the RHS, we take cube on both sides

• \(y^9 = y\)
Per our conceptual understanding, we know that this is possible only when \(y =0, -1\) or \(1\)

As \(y > 0\) is given, we get

• \(y = 1\)
As we got a unique value for ‘y’

Statement 1 alone is sufficient to answer this question.

Step 4: Analyze Statement 2 independently

As we don’t get a unique value for ‘y’

Statement 2 alone is NOT sufficient to answer this question.

Correct Answer: Option A

Note:

For Statement 2, many test-takers commit the mistake of dividing both sides of ay = a by ‘a’ thereby getting the answer as y = 1.
Please note that you are allowed to do this division only if a ≠0 is given as division by zero is not defined.

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

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pushpitkc · Answer

If y is a positive integer, what is the value of y?

(1)  y^3 = y^{1/3}

From this statement, since it has been given that y is positive, 
the only integer which satisfies this equation is 1. Hence, sufficient.

(2)  ay = a , and  a < 1

Since a<1, if a = 0, 
we can have any value for y, since all values of y 
will satisfy this equation, statement 2 alone is not sufficient. (Option A)

aishu0091 · Answer

Hi,

I am having difficulty with the second statement:

2) ay=a 
I take the a to the LHS 
ay-a=0
taking a as common 
a(y-1)=0
this is where I start to get confused-I'm not sure if this is even correct or I've got it completely messed up in my head but- 
a=0 or y-1=0 ---> y=1

If this is wrong could someone please help me with why and it would also be great if someone could confirm when to use the
a(y-1)=0 
a=0 or y-1=0 ---> y=1?

Many thanks!

MH321 · Answer

Statement-1: y³=y^(1/3) 
Since y is a positive integer, if y=1 then this satisfies this equation which results in 1³=1^(1/3) 
⇒1=1 
Therefore, S-1 is sufficient.

Statement-2: ay=a where a<1 
So a=0,–1,–2,...

If a<0 then y=1 but if a=0 y=0 
Therefore, S-2 is not sufficient.

Ans. is A

Rickooreoisb · Answer

1) y3=y1/3

whenever you are given this only values possible are 0,1,-1

here given that y is a positive integer, -1 is not possible ;  infact even 0 is not allowed

hence A is sufficient

If y is a positive integer, what is

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If y is a positive integer, what is

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