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10 Dec 2018, 02:32
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A
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What is the value of a positive integer x?
(1) x is three times the sum of its digits
(2) x is a two-digit number
M36-66
(1) x is three times the sum of its digits
(2) x is a two-digit number
M36-66
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anshkool4u
Current Student
Joined: 18 Oct 2018
Last visit: 22 Oct 2022
Posts: 91
Given Kudos: 23
Location: India
Concentration: Finance, Operations
Schools: IIMA PGPX'23 (A)
GMAT 1: 710 Q50 V36
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WE:Business Development (Retail Banking)
11 Dec 2018, 03:06
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Answer is A.
From stmnt 1,we know X=3*( sum of digits of X)
Now,supposing X is A3 digit no.,999,sum of digits =27,and 3 times 27= 81,a 2 digit no.which is contradictory in itself.
Considering X=100,sum of digits=1,hence 3 times 1=1,a one digit no.
This means X should be a 2 digit no.
Let X=10a+b
Then 10a+b= 3*(a+b)
Or 7a=2b,or a=3.5b.
Now,for the 2 digit no.X,a and b should both be integers,and should be 0<a,b<=9.
Only digits satisfying this are 2 and 7.
So,X=27= 3*(2+7)
Sufficient.
Stmnt 2 is insufficient
So,A
Posted from my mobile device
From stmnt 1,we know X=3*( sum of digits of X)
Now,supposing X is A3 digit no.,999,sum of digits =27,and 3 times 27= 81,a 2 digit no.which is contradictory in itself.
Considering X=100,sum of digits=1,hence 3 times 1=1,a one digit no.
This means X should be a 2 digit no.
Let X=10a+b
Then 10a+b= 3*(a+b)
Or 7a=2b,or a=3.5b.
Now,for the 2 digit no.X,a and b should both be integers,and should be 0<a,b<=9.
Only digits satisfying this are 2 and 7.
So,X=27= 3*(2+7)
Sufficient.
Stmnt 2 is insufficient
So,A
Posted from my mobile device
09 Nov 2021, 04:29
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Bunuel
Official Solution:
What is the value of a positive integer \(x\)?
(1) \(x\) is three times the sum of its digits
First let's check how many digit number \(x\) can be.
Can \(x\) be a single-digit number? No. Only 0 satisfices \(x=3x\) but we are told that \(x\) is positive.
Can \(x\) be a three-digit number? No. The maximum sum of the digits of a three-digit number is \(9+9+9=27\) and thrice of that is not a three-digit number. The same for four or more digit numbers: thrice the sum of the digits will always be less than the number itself.
Can \(x\) be a two-digit number? Say \(x=10a+b\), then we'd have that \(10a+b=3(a + b)\):
\(\frac{a}{b}=\frac{2}{7}\). Since both \(a\) and \(b\) are positive digits (1, 2, 3, 4, 5, 6, 7, 8, 9), then \(a=2\) and \(b=7\). So, \(x=27\). Sufficient.
(2) \(x\) is a two-digit number. Clearly insufficient.
Answer: A
