GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 25 Jan 2020, 20:36

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60647
If a is positive integer, can a be expressed as the product of two int  [#permalink]

### Show Tags

26 Dec 2016, 11:00
00:00

Difficulty:

45% (medium)

Question Stats:

55% (01:17) correct 45% (01:27) wrong based on 105 sessions

### HideShow timer Statistics

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

_________________
Intern
Joined: 18 Aug 2016
Posts: 2
If a is positive integer, can a be expressed as the product of two int  [#permalink]

### Show Tags

Updated on: 27 Dec 2016, 01:51
1
1
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

Originally posted by MG1788 on 26 Dec 2016, 23:12.
Last edited by MG1788 on 27 Dec 2016, 01:51, edited 2 times in total.
Manager
Joined: 22 May 2015
Posts: 124
Re: If a is positive integer, can a be expressed as the product of two int  [#permalink]

### Show Tags

18 Jun 2019, 17:52
1
OhsostudiousMJ wrote:
Bunuel wrote:
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

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

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

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.
_________________
Consistency is the Key
Current Student
Joined: 07 Mar 2015
Posts: 108
Location: India
Concentration: General Management, Operations
GMAT 1: 590 Q46 V25
GPA: 3.84
WE: Engineering (Energy and Utilities)
Re: If a is positive integer, can a be expressed as the product of two int  [#permalink]

### Show Tags

26 Dec 2016, 23:22
MG1788 wrote:
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 can be a decimal or integer
let a = 8.1 = 0.3*27 but x,y have to be >1
let a = 10.1 = 10.1*1 but x,y have to be >1
therefore not B

i) + ii)
a = even and lies between 7 & 11 =? a = 8,10. these can be represented as x*y with x,y>1

I think itc C

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
Marshall & McDonough Moderator
Joined: 13 Apr 2015
Posts: 1684
Location: India
Re: If a is positive integer, can a be expressed as the product of two int  [#permalink]

### Show Tags

27 Dec 2016, 01:05
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.

Current Student
Joined: 03 Oct 2012
Posts: 2
Schools: Babson '19 (A)
If a is positive integer, can a be expressed as the product of two int  [#permalink]

### Show Tags

27 Dec 2016, 08:55
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.
Marshall & McDonough Moderator
Joined: 13 Apr 2015
Posts: 1684
Location: India
Re: If a is positive integer, can a be expressed as the product of two int  [#permalink]

### Show Tags

27 Dec 2016, 09:55
jojo1 wrote:
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.

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.
Manager
Joined: 28 Jan 2019
Posts: 96
Location: India
GMAT 1: 700 Q49 V36
GPA: 4
WE: Manufacturing and Production (Manufacturing)
If a is positive integer, can a be expressed as the product of two int  [#permalink]

### Show Tags

18 Jun 2019, 05:45
Bunuel wrote:
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

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

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

_________________
"Luck is when preparation meets opportunity!"
Manager
Joined: 28 Jan 2019
Posts: 96
Location: India
GMAT 1: 700 Q49 V36
GPA: 4
WE: Manufacturing and Production (Manufacturing)
Re: If a is positive integer, can a be expressed as the product of two int  [#permalink]

### Show Tags

19 Jun 2019, 01:41
OhsostudiousMJ wrote:
Bunuel wrote:
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

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

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

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.

Okay, I get it now. Thanks.
_________________
"Luck is when preparation meets opportunity!"
LBS Moderator
Joined: 04 Jun 2018
Posts: 690
Location: Germany
Concentration: General Management, Finance
GMAT 1: 730 Q47 V44
GPA: 3.4
WE: Analyst (Transportation)
Re: If a is positive integer, can a be expressed as the product of two int  [#permalink]

### Show Tags

19 Jun 2019, 02:11
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.
_________________
Manager
Joined: 04 Jun 2017
Posts: 110
Location: India
Concentration: Strategy, Operations
GMAT 1: 500 Q39 V20
GPA: 3.82
Re: If a is positive integer, can a be expressed as the product of two int  [#permalink]

### Show Tags

19 Jun 2019, 09:55
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'

Intern
Joined: 22 May 2019
Posts: 11
Re: If a is positive integer, can a be expressed as the product of two int  [#permalink]

### Show Tags

15 Jan 2020, 01:39
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.

Re: If a is positive integer, can a be expressed as the product of two int   [#permalink] 15 Jan 2020, 01:39
Display posts from previous: Sort by