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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] New post 31 Jan 2012, 17:15
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A
B
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Difficulty:

  35% (medium)

Question Stats:

69% (01:48) correct 31% (01:02) wrong based on 71 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.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 31 Jan 2012, 17:38, edited 1 time in total.
Added the OA
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Re: 2 digit number x [#permalink] New post 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).

Hope it's clear.
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Status: Preparing for the 4th time -:(
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Re: 2 digit number x [#permalink] New post 31 Jan 2012, 17:37
You are too good. Thanks for the correction.
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MGMAT 1 --> 530
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Sum of Digits of Positive 2 two-digit number [#permalink] New post 27 May 2012, 14:59
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] New post 27 May 2012, 15:01
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] New post 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)

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Re: Sum of Digits of Positive 2 two-digit number [#permalink] New post 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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Sum of Digits of Positive 2 two-digit number   [#permalink] 28 May 2012, 04:47
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