If a is positive integer, can a be expressed as the product of two int

Question

If a is positive integer, can a be expressed as the product of two integers, each of which is greater than 1?

(1) a is even.
(2) 7 < a < 11

MG1788 · Answer

i) since a is even - it can only be a +ve integer.
if a = 2 = 2*1 but x,y have to be >1 therefore not A

ii) a is a +ve integer 
let a = 9 =3*3, but x,y have to be >1 (false)
let a = 8 = 4*2 or 8*1 (false)

B

vivekkumar987 · Answer

I agree till last line , but i think it is E

a = 8 or 10 : 8 = 4 * 2 here both are >1

8 = 8*1 here one integer is equal to 1

Kurtosis · Answer

Question: Is 'a' composite integer?

If 'a' is prime it cannot be expressed as a product of 2 integers, each of which is greater than 1.

St1: a is even --> If a = 2 then a is prime and cannot be expressed as a product of 2 integers which are greater than 1.
If a = 4 then 4 = 2*2 and can be expressed as product of 2 integers.
Not Sufficient.

St2: a = 8, 9, 10 --> a is not prime. a can be expressed as product of 2 integers which are greater than 1.
Sufficient.

Answer: B

jojo1 · Answer

IMO E

Given - a >0, a->integer
asked can a = b*c with b,c>1 and b,c integers

1) since a is even 
 Possible solutions
 (i) b=2, c=1 a=even
 a = 2*1 = 2 ( c not greater than 1 ) ---------NO
 (ii) b=2, c=3 a=even
 a = 2*3 = 6 -------------- YES

2) a = { 8,9,10 }
 Possible Solutions
 (i) b = 5 c = 2
 a= 5*2 = 10 ----------- YES ( B,C integers, >1 )
 (ii) b= 5/2 c=4
 a = 5/2 * 4 =10 -------------- NO ( B,C >1 but B is not an integer. But A still meets the criteria )

Therefore, Not A, not B

Combine (1) and (2) statements

Possible Solutions
 (i) b = 5 c = 2
 a= 5*2 =  10  ----------- YES ( B,C integers, >1 )
 (ii) b= 5/2 c=4
 a = 5/2 * 4 = 10  -------------- NO ( B,C >1 but B is not an integer)

A is  even  and a lies {8,9, 10 }
But we still have YES and NO answers.

Hence E.

Kurtosis · Answer

Hi  jojo1 ,

Question is not asking us to test whether a or b is a non integer. We have to check whether the integer can be expressed as a product of two integers greater than 1.

OhsostudiousMJ · Answer

Hi, the question asks if  a  "can" be expressed as.....

And in both the cases, of course,  a  can be expressed as asked.

Shouldn't the answer be D?

laddaboy · Answer

Well the first statement is not valid when a = 2. Ideally we say a statement is true when it is  valid for all the values , so here in this case say Can 2 be expressed as product of 2 ints both greater than 1? The answer is no , hence s1 is false.

OhsostudiousMJ · Answer

Okay, I get it now. Thanks.

Arro44 · Answer

I think the answer is B.

Statement 1 tells us that A has to be even, but an even integer allows for both scenarios:

Case 1: 2*3 = 6 = Product of two integers that are not 1
Case 2: 1*2 = 2 = Not possible to be formed by multiplying two positive integers that are not 1

Statement two tells us that a is not prime (no primes between 7 and 11)
Therefore, we know that "a" can be formed by multiplying two integers other than one.

MSIMBA · Answer

Given a = + ve integer 
Que = a can be expressed as c *b or not

1. A is even ,lets start with 2 = 2* no feasible value as value should be > 1 
 with 4 = 2 * 2 = feasible 
NOT SUFFICIENT 
2. 7 < a < 11 
 a = 2*4 , 2*5 , 4 * 2 , 5 *2 feasible
SUFFICIENT'

Answer is B

SuryaNouliGMAT · Answer

Given :
a=mn, where m & n are greater than 1 (m&n>1)
from st1 -> a is even i.e a = 2,4,6,8,10.....
lets take it one by one :
a = 2 ----> mn = 2 ----> 2*1 = 2 (not valid --> condition is m & n >1)
a = 4 ----> mn = 4 ----> 2*4 = 2 (valid)

from these solutions, we can see there is no consistency, so NOT SUFFICIENT

from st2 -> 7 < a < 11, which means values of a are {8,9,10}
lets take it one by one :
8 = possible factors = 1,2,4,8 = (1*8);(2*4);(4*2);(8*1) = 1 being factor of 8, makes it against the cond
& so not valid
9 = possible factors = 1,3,9 = (1*9);(3*3);(9*1) = 1 being factor of 9, makes it against the cond & so
not valid
10 = possible factors = 1,2,5,10 = (1*10);(2*5);(5*2);(10*1) = 1 being factor of 10, makes it against the cond & so not valid

so a ={8,9,10} results a STRICTLY NO

Note : In DS, either STRICTLY YES or STRICTLY NO results a SUFFIECIENT RESULT

Therefore B is Suffient.

Please correct me if my approach or my answer is wrong.

Thank and kudos in advance

If a is positive integer, can a be expressed as the product of two int

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

If a is positive integer, can a be expressed as the product of two int

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