GMAT Math : Whole number shortlisting

Let’s start with an example :

A room contains 101 people, given there is atleast 1 architect in the room, how many total architects are in the room?

  1. 32% of the architects are left handed
  2. 71% of the architects are bongo players

The key concept to this question and many such questions is that entities (such as girls, boys, motorcycles and architects) have to be whole numbers. The number of architects cannot be 12.5 or -7, it has to be whole positive number such as 0, 10, 17 or 100.

Let the number of architects be x. We know that 1 ≤ x ≤ 101 (given in the question statement)

From statement (1) – 32% of x has to be a whole positive number

32x/100 should be a whole positive number

Simplifying the above equation 8x/25 has to be whole positive number. Hence x has to be a multiple of 25 and 1 ≤ x ≤ 101. So x can be 25, 50, 75 and 100. Insufficient information as we are not able to fix one value of x.

Statement (2) tells us that 71% of x has to be a whole positive number

71x/100 has to be a whole positive number. Hence x has to be a multiple of 100 and 1 ≤ x ≤ 101. So x = 100 and we are able to determine the number of architects in the room. Sufficient information from statement (2) alone and hence we go with option (B).

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