Bunuel
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.
Kudos for a correct solution.
VERITAS PREP OFFICIAL SOLUTION: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.