If the sum of the digits of the positive two-digit number x is 4, what

Question

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.

Bunuel · Answer

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).

Hope it's clear.

enigma123 · Answer

You are too good. Thanks for the correction.

aazhar · Answer

OA is B.

Why can't x be 04?

Sum of 0 + 4 = 4
04 is positive

Does GMAT not recognize this style?

cyberjadugar · Answer

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)

Regards,

Bunuel · Answer

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.

pacifist85 · Answer

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.

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

2x<44 --> x<22. NS, as there are multiple options.

x<22 and odd. So, only 13 works.

anairamitch1804 · Answer

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.

seaninja90 · Answer

well my solution worked out like this

x can be written as= 10 a+b---1
we are given a+b = 4 -----2
2-1= 9a=x-4
only 13 fits the solution so A is sufficient , therefore D

Bunuel · Answer

My friend,

If you want to find out the OA, you can check under the spoiler in the original post. It's B, not D. Plus, you are quoting the very post which gives TWO values of x possible 13 AND 31. Both of them fit even your solution.

saukrit · Answer

Consider x =10*a+b

a+b= 4 (given). What is the value of x?

Before we analyze options let us find the possible values of x
x can be 13,22,31,40 (Since the sum of digits is 4 and it is a double digit number)

1) x is odd...x maybe 13 or 31...  Not sufficient . Strike off A, D
2) 2*x is less than 44.....x may be 13 only..(all other possible values give 2*x>=44) .  Hence B alone is Sufficient .

Answer is B

nivivacious · Answer

Let the digits of x be a and b
Given a + b = 4 
therefore a = b-4
X = 10a + b
Therefore X= 10(4-b)+b
X= 40-10b+b
X=40-9b
Also given: X is positive, and has 2 digits
To find: X

St1 : Does not help us much. hence not sufficient
St 2: 2X<44
Therefore X<22
40-9b<22
40-9(1) = 31
40-9(2) = 22
40-9(3)= 13
40-9(4) =4 
Therefore we can see that the only assumption that meets all values is 40-9(3)
Hence 
a+b=4
a+3=4
a=1
X=10a+b
X=13
Hence B is sufficient

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If the sum of the digits of the positive two-digit number x is 4, what

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If the sum of the digits of the positive two-digit number x is 4, what

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards