GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 05 Dec 2019, 22:05 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If pq/10 is an integer, is p/5 an integer? (1) q/2 is an integer

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 59561
If pq/10 is an integer, is p/5 an integer? (1) q/2 is an integer  [#permalink]

### Show Tags 00:00

Difficulty:   55% (hard)

Question Stats: 60% (01:40) correct 40% (01:41) wrong based on 112 sessions

### HideShow timer Statistics

If pq/10 is an integer, is p/5 an integer?

(1) q/2 is an integer

(2) p is a prime number
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5428
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If pq/10 is an integer, is p/5 an integer? (1) q/2 is an integer  [#permalink]

### Show Tags

Bunuel wrote:
If pq/10 is an integer, is p/5 an integer?

(1) q/2 is an integer

(2) p is a prime number

From 1: q/2 can be any integer value >/1
so pq/10 we can say
let q= 2 so now p has to be 5 to be valid so yes p/5 is an integer
let q=10, so now p has to be 1 , so p/5 is not an integer
In suficient

From 2:
P is a prime no. it can be ,3,2,7,, so again we would get yes at 5 and no at other no. in sufficient

Again when combining let p =3 and q= 10 so pq/10 is an integer and 3/5 "p/5" is not an integer and
at p=5, q=2 , p/5 is an integer hence E ....
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1415
Location: India
Re: If pq/10 is an integer, is p/5 an integer? (1) q/2 is an integer  [#permalink]

### Show Tags

1
Bunuel wrote:
If pq/10 is an integer, is p/5 an integer?

(1) q/2 is an integer

(2) p is a prime number

pq/10 can also be written as p/5 * q/2: this product is given to be an integer. We have to determine whether p/5 is an integer or not.

(1) q/2 is an integer. And product of this integer q/2 with p/5 is also an integer. Now in this case p/5 could be integer or it could be not.
Eg, say q/2 is 4, and p/5 is 1, then the product 4*1 is an integer. Or say q/2 is 4 and p/5 is 0.5, here also the product 4*0.5 is an integer.
So we cannot be sure whether p/5 is an integer or not.
Not sufficient.

(2) This is definitely not sufficient. Eg if p is 5, then p/5 is an integer. But if p is 2, then p/5 is not an integer. '
Not sufficient.

Combining the two statements, p is a prime number, q/2 is an integer, and the product of q/2 * p/5 is also integer.
So lets say, q/2 = 4, p=5. Here the product 4*5 is an integer, p is a prime number and p/5 is an integer.
Now lets say, q/2 = 5, p=2. Here the product 5*2 is an integer, p is a prime number BUT p/5 is NOT an integer.

Math Expert V
Joined: 02 Sep 2009
Posts: 59561
Re: If pq/10 is an integer, is p/5 an integer? (1) q/2 is an integer  [#permalink]

### Show Tags

Bunuel wrote:
If pq/10 is an integer, is p/5 an integer?

(1) q/2 is an integer

(2) p is a prime number

Director  P
Joined: 24 Nov 2016
Posts: 917
Location: United States
Re: If pq/10 is an integer, is p/5 an integer? (1) q/2 is an integer  [#permalink]

### Show Tags

Bunuel wrote:
If pq/10 is an integer, is p/5 an integer?

(1) q/2 is an integer

(2) p is a prime number

pq/10=integer… factors(p and/or q) may contain any multiples of 10

(1) q/2 is an integer: insufic.

q=2*anything;
q=2, p=5*anything, p/5=integer;
q=10, p=anything, p/5=anything;

(2) p is a prime number: insufic.

p=prime;
p=5, p/5=integer;
p=3, p/5≠integer;

(1 & 2): insufic.

q=10, p=3, p/5≠integer;
q=10, p=5, p/5=integer; Re: If pq/10 is an integer, is p/5 an integer? (1) q/2 is an integer   [#permalink] 18 Oct 2019, 11:04
Display posts from previous: Sort by

# If pq/10 is an integer, is p/5 an integer? (1) q/2 is an integer  