If d is a positive integer, is d^(1/2) greater than 15?

Given information= d is +ve integer

Question asked= \(\sqrt{d}\) > 15

or d>225

Any statement that gives us value of d will be sufficient to find the solution .

(1) d is divisible by 25.

d has 5*5. It can be 25, 50, and so on. Not sufficient.

(2) d is divisible by 40
d has 5 * 2*2*2 in it. It can be 40 , 80 and so on. not sufficient.

Combining both statements, d has LCM of 5*5*2*2*2= 200. So d can be 200, 400 and so on. Not Sufficient.

IMO, answer is E
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For Statement (1) : d could be 25 or 625 ,\(\sqrt{25}\) or 5<15 but \(\sqrt{625}\) or 25>15,Not Sufficient

For Statement (2) : d could be 40 or 1600,\(\sqrt{40}\) or<7 which is <15 but \(\sqrt{1600}\) or 40>15,Not Sufficient

Combining two Statements together we could find that d could be LCM of 25 and 40 or 200,so \(\sqrt{200}\)<15(since \(\sqrt{225}\)=15) but d could be LCM of 625 and 1600 or 25*25*64 ( also the LCM must be \(\geq{1600}\) because 1600 is the greatest number of the two numbers) too,So \(\sqrt{25*25*64}\) is definitely >15 .So the combination of two statements doesn't work

Correct Answer E

Taking Numbers would help.

Statement 1: d is divisible by 25

say d = 25; then d is divisible by 25, now \(\sqrt{25}\) = 5; it is less than 15
say d = 625; then d is divisible by 25, now \(\sqrt{625}\) = 25; it is greater than 15

Not sufficient.

Statement 1: d is divisible by 40

say d = 40; then d is divisible by 40, now \(\sqrt{40}\) = 2 * roughly (3.5), it is certainly less than 15
say d = 400; then d is divisible by 40, now \(\sqrt{400}\) = 20; it is greater than 15

Not sufficient.

Combining Statement 1 and 2: d is divisible by 40 and 25 both

Least value of such number would be 200 (LCM of 40 and 25).

say d = 200; then d is divisible by 40 and 25, now \(\sqrt{200}\) = 10 * 1.414, it is certainly less than 15
say d = 400; then d is divisible by 40 and 25, now \(\sqrt{400}\) = 20; it is greater than 15

Not sufficient.

Answer: E

Question
Is D> 225?
St:1
d is divisible by 25.
When d=25 answer is no
When d=250 answer is yes
Not sufficient

St-2
d is divisible by 40.
When d=40 answer is no
When d=400 answer is yes
Not sufficient

Combine:
D is divisible by 25 and 40
LCM of 25 and 40 =200
When d=200 answer is no
When d=1000 answer is yes
Ans: E

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