A child selected a three-digit number, XYZ, where X, Y, and Z denote

A child selected a three-digit number, XYZ, where X, Y, and Z denote the digits of the number. If no two of the three digits were equal, what was the three-digit number?

(1) The sum of the digits was 10.

There can be many combinations for 3 digit numbers, whose sum of the digits was 10.

Eg. 136, 901, 361.. etc. This statement is not sufficient.


(2) X < Y < Z

There can be many combinations for 3 digit numbers with the above condition

123, 345, 349.. etc. This statement is not sufficient.


combining both statements, we get

136, 127, 235.. etc. Hence both statements are also not sufficient.

Answer is E

So three distinct digits: x, y, z
We need to have values of x, y, z

Statement 1. x+y+z = 10
1+2+7 = 2+3+5 = 10.. More than one set of values depict that this statement is Insufficient

Statement 2. X<Y<Z
Many cases are possible. Clearly Insufficient

When we combine two statements, still we have more than one cases
Eg - 1, 2, 7 OR 2, 3, 5..
Clearly Not Sufficient

Hence answer is E

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Since we have 3 variables (X, Y and Z) and 0 equations, E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

X=1,Y=2,Z=3 and X=2,Y=3,Z=5 are possible solutions.

Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.