**Answer choices for data sufficiency questions Q11-19:**

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient

(E) Statements (1) and (2) TOGETHER are NOT sufficient

**Q11. While on a straight road, car X and car Y are traveling at different constant rates. If car X is now 1 mile ahead of car Y, how many minutes from now will car X be 2 miles ahead of car Y?**

(1) Car X is traveling at 50 miles per hour and car Y is traveling at 40 miles per hour.

(2) 3 minutes ago car X was ½ mile ahead of car Y.

*The word constant is key to this question. Speed = distance/time. The difference between their speed is 10 miles/hour. Statement one is sufficient in isolation. Statement two is also sufficient. The correct answer is (D).

**Q12. In what year was Ellen born?**

(1) Ellen’s brother Pete, who is 1.5 years older than Ellen, was born in 1956.

(2) In 1975 Ellen turned 18 years old.

*The correct answer is (B). Statement one is insufficient on it’s own to answer the question because Ellen’s brother may have been born in February or in August of 1956 leading to two different birth years for Ellen.

**Q13. What is the number of female employees in Company X?**

(1) If company X were to hire 14 more people and all of these people were females, the ratio of the number of male employees to the number of females employees would then be 16 to 9.

(2) Company X has 105 more male employees than female employees.

*Statement one states that (#of men)/(# of women + 14) = (16/9). In statement one we only have one linear equation and in statement two we also only have one linear equation. Statement two states that the (# of females + 105) = # of men. The correct answer here is (C). In combination they’re sufficient but in isolation they’re not.

**Q14. Is the integer x divisible by 36?**

(1) x is divisible by 12.

(2) x is divisible by 9.

*When you see the word divisible in the question, then you should immediately think about the prime factors of the numbers in the question. Think about the prime factors of 36, 12 and 9. In combination, 9 and 12 have all the numbers needed. The correct answer is (C).

**Q15. What is the average (arithmetic mean) of j and k?**

(1) The average (arithmetic mean) of j + 2 and k + 4 is 11.

(2) The average (arithmetic mean) of j, k and 14 is 10.

*The question is asking for the value of j and k together, but not independently. Statement one states that [(j + k + 6)/ 2] = 11. Statement two states that (j + k + 14)/ 3 = 10. Statements one and two are both sufficient independently, therefore the correct answer is (D).

**Q16. What is the value of a – b?**

(1) a = b + 4

(2) (a – b)2 = 16

*Statement one is sufficient. Statement two is not sufficient because that means that (a – b) has two possible values: +4 and -4. Whenever you see a square or a fourth, a number raised to an even exponent, then you should immediately be suspicious, because it is very likely that they want to trick you on the correct answer. The correct answer is (A).

**Q17. Is rst = 1?**

(1) rs = 1

(2) st =1

*Statements one and two in isolation are not sufficient. In combination, they look sufficient, but r could be 2 and s can be ½ and t can be 2. The correct answer is (E).

**Q18. In a certain office, 50 percent of the employees are college graduates and 60 percent of the employees are over 40 years old. If 30 percent of those over 40 have master’s degrees, how many of the employees over forty have master’s degrees?**

(1) Exactly 100 of the employees are college graduates.

(2) Of the employees forty years old or less, 25 percent have master’s degreses.

*Statement one is sufficient; it allows usto determine the number of employees in the company. There are 200 employees in the company and 120 of them are over 40 years old. Statement two in isolation doesn’t contain information of the total number of employees that the company has; therefore, we cannot calculate the number of employees over 40 years old that have master degrees. The correct answer is (A).

**Q19. Is xy < 6?**

(1) x < 3 and y < 2.

(2) ½ < x < 2/3 and y^2 < 6.

*The key with statement one is that whenever you see an inequality in a data sufficiency question, you always want to think about the number line. If x is 2 and y is 1, then that’s less than 6, but x could be -3 and y can also be -3 so x times y is 9 and that’s greater than 6, so statement one is not sufficient. We have to remember that when we see an even exponent that there are two possible values for it. The correct answer is (B).