Positive integer y is a perfect square such that y is the product of 16, 9, 7 and r. Which of the following could be a value of r?
A. 2
B. 3
C. 5
D. 7
E. 9
Question on Perfect Square 5
This topic has expert replies
- richachampion
- Legendary Member
- Posts: 698
- Joined: Tue Jul 21, 2015 12:12 am
- Location: Noida, India
- Thanked: 32 times
- Followed by:26 members
- GMAT Score:740
R I C H A,
My GMAT Journey: 470 → 720 → 740
Target Score: 760+
[email protected]
1. Press thanks if you like my solution.
2. Contact me if you are not improving. (No Free Lunch!)
My GMAT Journey: 470 → 720 → 740
Target Score: 760+
[email protected]
1. Press thanks if you like my solution.
2. Contact me if you are not improving. (No Free Lunch!)
- richachampion
- Legendary Member
- Posts: 698
- Joined: Tue Jul 21, 2015 12:12 am
- Location: Noida, India
- Thanked: 32 times
- Followed by:26 members
- GMAT Score:740
OA: D
R I C H A,
My GMAT Journey: 470 → 720 → 740
Target Score: 760+
[email protected]
1. Press thanks if you like my solution.
2. Contact me if you are not improving. (No Free Lunch!)
My GMAT Journey: 470 → 720 → 740
Target Score: 760+
[email protected]
1. Press thanks if you like my solution.
2. Contact me if you are not improving. (No Free Lunch!)
- fiza gupta
- Master | Next Rank: 500 Posts
- Posts: 216
- Joined: Sun Jul 31, 2016 9:55 pm
- Location: Punjab
- Thanked: 31 times
- Followed by:7 members
Y(perfect square) = 16*9*7*r
16 and 9 are perfect square but not 7
so value of r will be 7 or multiple of 7
r = 7 or r = 7z(z should be perfect square)(7*4, 7*9....)
only option D satisfies
16 and 9 are perfect square but not 7
so value of r will be 7 or multiple of 7
r = 7 or r = 7z(z should be perfect square)(7*4, 7*9....)
only option D satisfies
Fiza Gupta
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi richachampion,
When you prime-factor a perfect square, each of the prime factors MUST show up an EVEN number of times...
eg. 9 = (3)(3) here, there are TWO 3s.
eg. 100 = (2)(2)(5)(5) here, there are TWO 2s and TWO 5s
eg. 16 = (2)(2)(2)(2) = here, there are FOUR 2s
Etc.
We're told that Y is a perfect square that is the product of 16, 9, 7 and R. Thus, prime-factoring Y will get us...
Y = (16)(9)(7)(R)
Y = (2)(2)(2)(2)(3)(3)(7)(R)
We have FOUR 2s and TWO 3s, but only ONE 7. We need there to be an even number of 7s, so the R must contain at least a '7.'
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
When you prime-factor a perfect square, each of the prime factors MUST show up an EVEN number of times...
eg. 9 = (3)(3) here, there are TWO 3s.
eg. 100 = (2)(2)(5)(5) here, there are TWO 2s and TWO 5s
eg. 16 = (2)(2)(2)(2) = here, there are FOUR 2s
Etc.
We're told that Y is a perfect square that is the product of 16, 9, 7 and R. Thus, prime-factoring Y will get us...
Y = (16)(9)(7)(R)
Y = (2)(2)(2)(2)(3)(3)(7)(R)
We have FOUR 2s and TWO 3s, but only ONE 7. We need there to be an even number of 7s, so the R must contain at least a '7.'
Final Answer: D
GMAT assassins aren't born, they're made,
Rich