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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, 17:15

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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.

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]

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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)

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, 07:36

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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, 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.

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

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20 Mar 2016, 22:39

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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, 01:17

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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Thanks & Regards, Anaira Mitch

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Re: If the sum of the digits of the positive two-digit number x
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29 Dec 2016, 01:17

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