|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
01 Jul 2020, 03:59
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
62% (01:07) correct
38%
(01:27)
wrong
based on 95
sessions
History
Date
Time
Result
Not Attempted Yet
If d is a positive integer, is \(\sqrt{d}\) an integer?
(1) d has an odd number of positive divisors.
(2) d has 3 positive divisors.
(1) d has an odd number of positive divisors.
(2) d has 3 positive divisors.
If positive integer d equal to the square of an integer?
(1) d has an odd number of divisors.
(2) d has 3 divisors.
(1) d has an odd number of divisors.
(2) d has 3 divisors.
01 Jul 2020, 04:10
Kudos
Bookmarks
If d is a positive integer, (d)^1/2 is an integer if d all prime factors of d have even power.
St. 1:
d = a^p * b^q .....
=> Number of factors of d = (p+1)(q+1)...
If number of factors = odd
=> (p+1)(q+1)... = odd
=> p, q ... are even
=> d = a^2n * b^2m...
=> d^1/2 = a^n * b^m...
=> d^1/2 is an integer.
=> St. 1 is sufficient.
St. 2:
d has three positive divisors
=> d = a^2
=> d^1/2 is an integer
=> St. 2 is sufficient.
Answer: D
Posted from my mobile device
St. 1:
d = a^p * b^q .....
=> Number of factors of d = (p+1)(q+1)...
If number of factors = odd
=> (p+1)(q+1)... = odd
=> p, q ... are even
=> d = a^2n * b^2m...
=> d^1/2 = a^n * b^m...
=> d^1/2 is an integer.
=> St. 1 is sufficient.
St. 2:
d has three positive divisors
=> d = a^2
=> d^1/2 is an integer
=> St. 2 is sufficient.
Answer: D
Posted from my mobile device
VIkash1073
Joined: 01 Jan 2020
Last visit: 06 Jul 2025
Posts: 3
Given Kudos: 7
Location: India
Schools: Broad Darden '24 ISB '23 Mendoza Tepper '24
GMAT 1: 680 Q49 V32
01 Jul 2020, 04:12
Kudos
Bookmarks
If d is a positive integer, is an integer?
(1) d has an odd number of positive divisors.
(2) d has 3 positive divisors.
Statement 1:
As only perfect squares have odd no. of divisors, hence sufficient.
Statement 2:
3 positive divisors - again odd no. of divisors, perfect square.
Example: 4 - divisors (1,2,4)
9- divisors (1,3,9)
25 - divisors (1,5,25) and so on
Sufficient.
Hence (D)
Posted from my mobile device
(1) d has an odd number of positive divisors.
(2) d has 3 positive divisors.
Statement 1:
As only perfect squares have odd no. of divisors, hence sufficient.
Statement 2:
3 positive divisors - again odd no. of divisors, perfect square.
Example: 4 - divisors (1,2,4)
9- divisors (1,3,9)
25 - divisors (1,5,25) and so on
Sufficient.
Hence (D)
Posted from my mobile device
