If x and y are integers and their sum is 23, is y ≥ 9?

Question

(1) x – 6 < 9
(2) x^3 = 2,744

Kudos for a correct  solution .

thembaseeker · Answer

x+y=23-----(i) Statement 1: x-6<9 ---> x<15 Hence x can have values like 14,13,12,...........and so on Substituting the value of x in equation (i) will lead to value of y as 9,10,11........and so on. Sufficient. Statement 2: x^3 = 2,744 =>x=14 From equation (i) y=9 Sufficient Answer: D

GMATinsight · Answer

Given : x+y = 23

Question  : Is y ≥ 9?  
i.e.    Question  : Is x  <  23-9 i.e. Is x  <  14?

Statement 1 : x – 6 < 9 
i.e. x < 9+6
i.e. x < 15
i.e. x  <  14. Hence,
SUFFICIENT

Statement 2 : x^3 = 2,744 
i.e. we have certain value of x which will render a certain value of y. Hence,
SUFFICIENT

Answer: option D

manishkhare · Answer

x+y=23 . y=23-x From Option A : x-6<9 so x <15 Maximum value of x=14 .so y =9 For all other values of x y>9 A is sufficient From Option B: x^3=2744 --> x=14 so y=9 Option b is sufficient Correct answer is D

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No.  The question asks: “Is y greater than or equal to 9?”

Given information in the question stem or diagram: x and y are integers and x + y = 23. Note: When specific information like this is given in the question stem, make sure you carefully leverage it with each statement.

Statement 1: x – 6 < 9. Adding 6 to both sides you see that x < 15. Since the question asks about y, substitute from the equation into the inequality. If x + y = 23, then x = 23 – y and, after substituting into the inequality, 23 – y < 15. Move y from the left to right and 15 from the right to left to see that y > 8. Since y must be an integer, this proves that y must be at least 9 and this information is sufficient. You could also do this logically, but algebraic manipulation leaves no doubt in your mind! This statement is sufficient so the answer is A or D. Note: In any problem that mixes equations and inequalities, do not forget that you can substitute from the equation into the inequality.

Statement 2: x^3 = 2744. It is tempting in this statement to try to find the cube root of 2,744 to get an exact value for x. However, since doing this will give you one value for x and since you can then subtract that value from 23 and get an exact value for y, this must be sufficient. Whatever value you find for y will either be “yes, greater than/ equal to 9” or “no, less than 9.” There is no need to do the math here and that is certainly the trick in this statement.  The correct answer is D . Note: This second statement is testing exclusively if you understand the concept of sufficiency and how it applies to each of the two question types. If you are missing this type of question (or spending lots of extra time on it!) review the rules/drills relating to sufficiency at the beginning of the book.

bumpbot · Answer

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If x and y are integers and their sum is 23, is y ≥ 9?

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If x and y are integers and their sum is 23, is y ≥ 9?

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