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(1) The sum of the two digits is 4. (2) The difference between the two digits is 2.

Kudos for a correct solution.

Question : If x= ab where a and b are tens and units digit respectively then find x?

Statement 1: a+b=4 x may be 13 or 22 or 31. Hence, NOT SUFFICIENT

Statement 2: a-b = 2 or b-a=2 if a-b=2 then x = 31 if b-a=2 then x = 13. Hence, NOT SUFFICIENT

Combining the two statements x may still be 13 or 31 Hence, NOT SUFFICIENT

Answer: option E
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Question Type: What Is the Value? This question asks for the value of the two-digit number x.

Given information in the question stem or diagram: x is a two-digit number.

Statement 1: The sum of the two digits is 4. There are only four two-digit numbers that have digits that total 4. They are 13, 22, 31, and 40. Since that allows for more than one value for x, this statement is not sufficient. Eliminate choices A and D.

Statement 2: The difference between the two digits is 2. This means that for the tens digit (T) and the units digit (U), either: T – U = 2, or U – T = 2. Many people confuse this statement and think that the tens digit must be larger, such as 64, where T – U = 2. However, 46 would also be acceptable since the difference between the digits is 2. Clearly this statement is not sufficient alone as there are many two-digit numbers where T – U = 2 or U – T = 2. Eliminate choice B.

Together: When taking the statements together it is best to start with the more limiting statement. Statement 1 only allows four values: 13, 22, 31, and 40. How many of these values are compatible with Statement 2? Two of them: 31 is T – U = 2; and 13 is U – T = 2. They each have a difference of 2. Since there are still two possible values for the two-digit number x, the correct answer is E. Note: This is a classic C vs. E problem. Almost everyone gets it down to choice C or E, but many people forget to differentiate between 13 and 31. (They either miss one in their list of possibilities for the first statement or assume that it must be 31 for the reasons discussed above.) Remember to do your best to exhaust all possibilities before picking answer C.
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Re: What is the value of the two-digit number x? [#permalink]

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05 Feb 2016, 15:51

I totally follow how you get to (e). but dsn't "1 minus 3" = -2??? If the test meant for us to consider 13, would it not have stated "the difference between the two digits is |2|"??? or am i overthinking.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the value of the two-digit number x?

(1) The sum of the two digits is 4. (2) The difference between the two digits is 2.

In the original condition, it is two-digit integer, which makes 2 variables. You need 2 equations in order to match with the number of equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. When 1) & 2), 13 and 31 are derived, which is not unique and not sufficient. Therefore, the answer is E.

-> For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: What is the value of the two-digit number x? [#permalink]

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22 Oct 2017, 07:10

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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