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If the sum of the digits of the positive two-digit number x [#permalink]
31 Jan 2012, 17:15
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This post was BOOKMARKED
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Difficulty:
25% (medium)
Question Stats:
66% (01:57) correct
34% (01:04) wrong based on 181 sessions
If the sum of the digits of the positive two-digit number x is 4, what is the value of x?
(1) x is odd. (2) Twice the value of x is less than 44.
As OA is not given, I have got B. Please can I request to see my solution below and confirm whether its correct or not ?
Statement 1 --> x is ODD so x can be 13 and 31. Two values, therefore insufficient.
Statement 2 --> When x is 13 then twice the value will be 26 and when x is 31 it will be 62. But x cannot be 62 as the statement 2 says Twice the value of x is less than 44. Therefore x has to be 13. Hence B is my answer choice.
Re: 2 digit number x [#permalink]
31 Jan 2012, 17:34
Expert's post
1
This post was BOOKMARKED
enigma123 wrote:
If the sum of the digits of the positive two-digit number x is 4, what is the value of x?
(1) x is odd. (2) Twice the value of x is less than 44.
As OA is not given, I have got B. Please can I request to see my solution below and confirm whether its correct or not ?
Statement 1 --> x is ODD so x can be 13 and 31. Two values, therefore insufficient.
Statement 2 --> When x is 13 then twice the value will be 26 and when x is 31 it will be 62. But x cannot be 62 as the statement 2 says Twice the value of x is less than 44. Therefore x has to be 13. Hence B is my answer choice.
If the sum of the digits of the positive two-digit number x is 4, what is the value of x?
x can take the following 4 values: 13, 31, 22, or 40.
(1) x is odd --> x can still take two values: 13 or 31. Not sufficient.
(2) Twice the value of x is less than 44 --> only 13 satisfies this statement, so x=13. Sufficient.
Answer: B.
P.S. Your solution seems fine, except there are 4 values of x possible not just 2 (though this doesn't affect the answer in our case).
Re: Sum of Digits of Positive 2 two-digit number [#permalink]
27 May 2012, 20:51
Hi aazhar,
The questions states that x is a two digit number, which can be in form of ab (\(a>0, b >=0\)) Also, a+b=4
using (1), x is odd => b is odd; (a,b) = (1,3),(3,1), two possibilities. Insufficient.
using (b), \(2x < 44\) or \(x < 22\) numbers will be 11,12,13,14,15,16,17,18,19,20,21 out of which only 13 has sum of digits as 4. x is 13. Sufficient.
If we make 10th place digit as zero, the number reduces to single digit. (and thus, it can't be 04)
Re: Sum of Digits of Positive 2 two-digit number [#permalink]
28 May 2012, 04:47
Expert's post
aazhar wrote:
OA is B.
Why can't x be 04?
Sum of 0 + 4 = 4 04 is positive
Does GMAT not recognize this style?
We are told that x is a two-digit integer, whereas 04 is just 4 so its a single-digit integer. For a complete solution please refer to the posts above. _________________
Re: If the sum of the digits of the positive two-digit number x [#permalink]
27 Oct 2014, 07:36
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Re: If the sum of the digits of the positive two-digit number x [#permalink]
14 Feb 2015, 03:25
Great! What I did was to assign values for x and its digits like this:
x=ab. We know from the stem that a+b=4.
[1] x is odd. NS, as there are 2 options. There are 5 ways in which a+b=4, namely: 4+0, gives the 2 digit #40, even 3+1, gives the 2 digit #31, odd 2+2, gives the 2 digit #22, even 1+3, gives the 2 digit #13, odd 0+4, gives the #4, single digit and even
[2] 2x<44 --> x<22. NS, as there are multiple options.
[1,2] x<22 and odd. So, only 13 works.
gmatclubot
Re: If the sum of the digits of the positive two-digit number x
[#permalink]
14 Feb 2015, 03:25
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