BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Arithmetic

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 181
Joined: Sat Oct 16, 2010 1:57 pm
Thanked: 4 times

Arithmetic

by N:Dure » Sun Dec 12, 2010 11:05 am
n and p are integers greater than 1

5n is the square of a number

75np is the cube of a number.

The smallest value for n + p is

A. 14
B. 18
C. 20
D. 30
E. 50
Top
Source: — Problem Solving |
User avatar
Community Manager
Posts: 991
Joined: Thu Sep 23, 2010 6:19 am
Location: Bangalore, India
Thanked: 146 times
Followed by:24 members

by shovan85 » Sun Dec 12, 2010 11:30 am
N:Dure wrote:n and p are integers greater than 1

5n is the square of a number

75np is the cube of a number.

The smallest value for n + p is

A. 14
B. 18
C. 20
D. 30
E. 50
5n is a square => n = 5 (lowest value)

75np is a cube
75 = 3 * 5^2 then np = 3^2*5 = 45 (lowest value)
then taking n = 5 p = 9

Thus n + p = 14

IMO A
If the problem is Easy Respect it, if the problem is tough Attack it
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1179
Joined: Sun Apr 11, 2010 9:07 pm
Location: Milpitas, CA
Thanked: 447 times
Followed by:88 members

by Rahul@gurome » Sun Dec 12, 2010 11:50 am
Minimum value of 5n such that it is a square of an integer = 25. Thus minimum possible value of n = 5

75np = (3)*(5²)*(n)*(p)
After placing the minimum possible value of n, 75np = (3)*(5³)*(p)

Thus minimum possible value of 75np such that it is cube of an integer is (3³)*(5³). Thu minimum possible value of p is 3² = 9

Minimum possible value of (n + p) = (5 + 9) = 14

The correct answer is A.
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Top
Master | Next Rank: 500 Posts
Posts: 181
Joined: Sat Oct 16, 2010 1:57 pm
Thanked: 4 times

by N:Dure » Sun Dec 12, 2010 12:28 pm
shovan85 wrote:
N:Dure wrote:n and p are integers greater than 1

5n is the square of a number

75np is the cube of a number.

The smallest value for n + p is

A. 14
B. 18
C. 20
D. 30
E. 50
5n is a square => n = 5 (lowest value)

75np is a cube
75 = 3 * 5^2 then np = 3^2*5 = 45 (lowest value)
then taking n = 5 p = 9

Thus n + p = 14

IMO A
Thanks Shovan!
Minimum value of 5n such that it is a square of an integer = 25. Thus minimum possible value of n = 5

75np = (3)*(5²)*(n)*(p)
After placing the minimum possible value of n, 75np = (3)*(5³)*(p)

Thus minimum possible value of 75np such that it is cube of an integer is (3³)*(5³). Thu minimum possible value of p is 3² = 9

Minimum possible value of (n + p) = (5 + 9) = 14

The correct answer is A.
Thanks Rahul, but I don't get this part: "Thus minimum possible value of 75np such that it is cube of an integer is (3³)*(5³). Thu minimum possible value of p is 3² = 9" ?
Top
User avatar
Community Manager
Posts: 991
Joined: Thu Sep 23, 2010 6:19 am
Location: Bangalore, India
Thanked: 146 times
Followed by:24 members

by shovan85 » Sun Dec 19, 2010 9:09 pm
5n is a square => n = 5 (lowest value)

75np is a cube
75 = 3 * 5^2 then np = 3^2*5 = 45 (lowest value)
then taking n = 5 p = 9

Thus n + p = 14
n = 5

We know 75np is a cube of an integer.

Now we have the LOWEST value of n=5, put this value in 75np.

Thus, 75np becomes 75*5*p.

Hence, 375p is a cube.

Factorize 375 to know what can be the minimum integer required to be mulitplied to 375 to make 375p a perfect cube.

375 = 125 * 3 = (5^3) * 3

From factorization we can see that 5 already have a power of 3, So it is already in the form of a cube. We need 3 to be in a perfect cube. To get 3 in the perfect cube from 3^2 = 9 is needed to be multiplied.

Thus p = 9
If the problem is Easy Respect it, if the problem is tough Attack it
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

Re: Arithmetic

by Scott@TargetTestPrep » Sun Mar 15, 2020 7:25 am
N:Dure wrote: ↑
Sun Dec 12, 2010 11:05 am
 n and p are integers greater than 1

5n is the square of a number

75np is the cube of a number.

The smallest value for n + p is

A. 14
B. 18
C. 20
D. 30
E. 50
The smallest value for n is 5.

Recall that a perfect cube has prime factors that must each be raised to a multiple of 3. We will use this fact to solve for p.

So 75np = 375p, and since 375p = 5^3 x 3p is a cube, we see that the smallest value for p is 9 (notice that 375p = 5^3 x 3^3). Therefore, the smallest value for n + p is 5 + 9 = 14.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1