What is the HCF of P and Q if 3P – Q – 5 = 0 and P and Q are positive integers?

This topic has expert replies
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members
What is the HCF of P and Q if 3P – Q – 5 = 0 and P and Q are positive integers?

1) P is completely divisible by 5.
2) Q is completely divisible by 5.



OA D

Source: e-GMAT

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members
BTGmoderatorDC wrote:
Sun Feb 16, 2020 5:17 pm
What is the HCF of P and Q if 3P – Q – 5 = 0 and P and Q are positive integers?

1) P is completely divisible by 5.
2) Q is completely divisible by 5.

OA D

Source: e-GMAT
Let's take each statement one by one.

1) P is completely divisible by 5.

Say P = 5x.

From 3P – Q – 5 = 0, we have 3*5x – Q – 5 = 0 => 15x – Q – 5 = 0

=> Q = 5(3x – 1)

Case 1: Say x is even, then 3x – 1 = odd; thus, HCF of P = 5x and Q = 5(3x – 1) is 5 since x and (3x – 1) are co-prime.

Case 2: Say x is odd, then 3x – 1 = even; thus, HCF of P = 5x and Q = 5(3x – 1) is 5 since x and (3x – 1) are co-prime.

Sufficient.

2) Q is completely divisible by 5.

With the same reasoning as done in Statement 1, we get HCF = 5. Sufficient.

The correct answer: D

Hope this helps!

-Jay
_________________
Manhattan Review

Locations: Manhattan Review Himayatnagar | GMAT Prep Hyderabad | GRE Prep Bangalore | Chennai GRE Coaching | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.