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# If the sum of the digits of the positive two-digit number x

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If the sum of the digits of the positive two-digit number x [#permalink]

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31 Jan 2012, 18:15
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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.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 31 Jan 2012, 18:38, edited 1 time in total.
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Re: 2 digit number x [#permalink]

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31 Jan 2012, 18:34
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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.

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).

Hope it's clear.
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Re: 2 digit number x [#permalink]

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31 Jan 2012, 18:37
You are too good. Thanks for the correction.
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Sum of Digits of Positive 2 two-digit number [#permalink]

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27 May 2012, 15:59
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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.
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Re: Sum of Digits of Positive 2 two-digit number [#permalink]

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27 May 2012, 16:01
OA is B.

Why can't x be 04?

Sum of 0 + 4 = 4
04 is positive

Does GMAT not recognize this style?
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Re: Sum of Digits of Positive 2 two-digit number [#permalink]

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27 May 2012, 21:51
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)

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Re: Sum of Digits of Positive 2 two-digit number [#permalink]

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28 May 2012, 05:47
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.
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Re: If the sum of the digits of the positive two-digit number x [#permalink]

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27 Oct 2014, 08:36
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Re: If the sum of the digits of the positive two-digit number x [#permalink]

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14 Feb 2015, 04:25
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.
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Re: If the sum of the digits of the positive two-digit number x [#permalink]

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20 Mar 2016, 23:39
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Re: If the sum of the digits of the positive two-digit number x [#permalink]

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29 Dec 2016, 02:17
If the sum of the digits of the positive two-digit number x is 4, then x must be 13, 31, 22, or 40. We can rephrase this question as “Is the value of x 13, 31, 22 or 40?”

(1) INSUFFICIENT: If x is odd, x can be 13 or 31.

(2) SUFFICIENT: From the statement, 2*x < 44, so x < 22. This means that x must be 13.

The correct answer is B.
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Re: If the sum of the digits of the positive two-digit number x   [#permalink] 29 Dec 2016, 02:17
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# If the sum of the digits of the positive two-digit number x

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