GMAT QUESTION 51,52

At least 100 students in a school study Japanese. 4% of students who study French also study Japanese. Do more students study French than Japanese?  (1) 16 students study both French and Japanese  (2) 10% of students at school who study Japanese also study French.

Solution:
Let J be the number of students studying Japanese and F be the number of students studying French.  Given information in the main statement:  J >= 100  0.04F study Japanese and French.  Question: Is F > J?
 Statement 1: Students studying J and F is 16. Therefore, 0.04F = 16, or  F = 400. This is insufficient, because J could be 100, in which case the answer to the question in the main stem is Yes, or J = 500, in which case J>F and the answer to the question is NO. INSUFFICIENT.  Statement 2: The algebraic translation of this statement is: 0.1 J = 0.04 F or F = 2.5 J, therefore F > J. SUFFICIENT.

A box contains identical balls in three different colors - Black, white and blue. There are 8-x blue balls and 2X+5 black balls. If a ball is picked at random from the box, what is the probability that the ball is either blue or black?
1) X=2  2) There are 3X+39 white balls in the box.

Solution:
1] X=2, clearly insufficient  2] Total balls = 3x+39 + 8-x + 2X+5 = 4x + 52 = 4[x+13]  Probability of getting either a blue or a black ball = [8-x + 2x + 5] / 4[x+13]  = [x+13]/4[x+13] = 1/4. Sufficient. Choice B.