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Difficulty:
45%
(medium)
Question Stats:
63% (01:56) correct
37%
(02:11)
wrong
based on 70
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Is \((50 + 5n)/n^2\) an integer
(1) n/5 is a positive integer
(2) n/10 is a positive integer
(1) n/5 is a positive integer
(2) n/10 is a positive integer
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
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Is (50+5n)/n^2 = Integer ?
or is (50/n^2) +5/n =integer?
(St1) n/5 is a positive integer
.: n= 5(k) where k>0 ,when k=1
Then YES (50+25)/25 =integer
when k=3 ,Then NO (50+5(15))/(15^2) is not integer
(Not suff)
(St2) n/10 is a positive integer
.: n= 10(k) where k>0 ,when k=1
Then YES (50+5(10))/(10^2)=integer
When k=3 then NO (50+5(30))/(30^2) is not an integer
(Not suff)
(St1+2) n is divisible by 10 and 5 so at least n=10(k) now ,the same situation as in (st2) YES /NO (not suff)
Answer E
Posted from my mobile device
or is (50/n^2) +5/n =integer?
(St1) n/5 is a positive integer
.: n= 5(k) where k>0 ,when k=1
Then YES (50+25)/25 =integer
when k=3 ,Then NO (50+5(15))/(15^2) is not integer
(Not suff)
(St2) n/10 is a positive integer
.: n= 10(k) where k>0 ,when k=1
Then YES (50+5(10))/(10^2)=integer
When k=3 then NO (50+5(30))/(30^2) is not an integer
(Not suff)
(St1+2) n is divisible by 10 and 5 so at least n=10(k) now ,the same situation as in (st2) YES /NO (not suff)
Answer E
Posted from my mobile device
utkarshg97
Joined: 26 Jun 2019
Last visit: 29 Oct 2022
Posts: 34
Location: India
Schools: Crosby Trulaske"19 IIM-A"19 (D)
GMAT 1: 660 Q51 V29
GPA: 3.3
Is (50+5n)/n^2 an integer?
(1) n/5 is a positive integer
(2) n/10 is a positive integer
(i) Checking for n/5 being a positive integer.
Let n/5 = k
=> n = 5k
now replacing n = 5k in the original equation.
We get, (50 + 5(5k))/25k^2
=> (50 + 25k)/25k^2
Now on splitting the numberator => (50/25k^2) + (25k/25k^2)
=> 2/k^2 + 1/k
(Not sufficient as we have k in the denominator.)
(ii) Now checking for n/10 being a positive integer.
Let n/10 = k
=> n = 10k
now replacing n = 10k in the original equation.
We get, (50 + 5(10k))/100k^2
=> (50 + 50k)/100k^2
Now on splitting the numberator => (50/100k^2) + (50k/100k^2)
=> 1/2k^2 + 1/2k
(Not sufficient as we have k in the denominator.)
And as per (ii) n is divisible by 10 which means it is already divisible by 5 means both equations together are also insufficient.
Hence ans is [E] :D
___________
Please drop in a kudos if it makes sense to you!
(1) n/5 is a positive integer
(2) n/10 is a positive integer
(i) Checking for n/5 being a positive integer.
Let n/5 = k
=> n = 5k
now replacing n = 5k in the original equation.
We get, (50 + 5(5k))/25k^2
=> (50 + 25k)/25k^2
Now on splitting the numberator => (50/25k^2) + (25k/25k^2)
=> 2/k^2 + 1/k
(Not sufficient as we have k in the denominator.)
(ii) Now checking for n/10 being a positive integer.
Let n/10 = k
=> n = 10k
now replacing n = 10k in the original equation.
We get, (50 + 5(10k))/100k^2
=> (50 + 50k)/100k^2
Now on splitting the numberator => (50/100k^2) + (50k/100k^2)
=> 1/2k^2 + 1/2k
(Not sufficient as we have k in the denominator.)
And as per (ii) n is divisible by 10 which means it is already divisible by 5 means both equations together are also insufficient.
Hence ans is [E] :D
___________
Please drop in a kudos if it makes sense to you!
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