Is x negative? (1) x^2 + 25 = 89 (2) x^3

Question

Is x negative?

(1) x^2 + 25 = 89

(2) x^3 < x

Kudos for a correct  solution .

VenoMfTw · Answer

IMO : C

St 1: x^2 + 25 = 89

x^2 = 64
Thus x = +8 or -8 
 Nt suff

St 2: x^3 < x

It is possible when 0<x<1 and when x<-1
 Nt suff

Combined:

x = -8.
hence Suff

KS15 · Answer

(1) x^2 + 25 = 89: x=8 or -8. Insufficient
(2) x^3 < x. If x=1/2, x^3<x and if x=-1/2, then x<x^3. Insufficient.

Using both statements, only x=-8 satisfies.
Answer C

lipsi18 · Answer

Is X= + or -ve?
1. X^2 = 64 therefore x can be -8 or +8 so insufficient
2. x(x^2-1)<0 so when x=-ve then x^2>1 or x>+1 or -1; or when x= +ve; x^2<1, so x<-1 or +1; non sufficient
1+2 only value it satisfies ais x=-ve and x is more than +1 and -1.
Hence answer is C

Bunuel · Answer

KAPLAN OFFICIAL SOLUTION:

Whenever we see exponents, we have to fight the temptation to assume that our variable is a positive integer. Remember that when exponents are involved, negatives and values between 0 and 1 are special. For statement (1), which simplifies to x^2 = 64, we have to remember that positives and negatives “go positive” when squared. Since 8 and -8 are both permissible, we don’t have sufficient information to determine whether x is negative. For Statement (2), positive integers (such as 4 or 6) aren’t permissible because cubing increases the original numbers. But let’s try different kinds of numbers. A negative number such as -2 will produce a situation in which x^3<x, so x could be negative. But don’t forget about, say, ½. That produces a smaller number when cubed as well! So x could be positive. Insufficient.

Combine the information, and you’ll see that there is only one permissible number, -8,  so the answer is (C) . An exponent is a great trigger that tells us to consider the impact of special numbers.

But let’s say you look a problem and you know that you need to pick different kinds of numbers, but you don’t know which numbers will be important. Do I need to consider negatives here? What about non-integers? Well, here is a list of seven numbers that help us cover our bases and stay strategic (with thanks to expert Kaplan GMAT teacher Adam Maze!):

-2, -1, -½, 0, ½, 1, and 2.

Think about it. In these seven numbers, you have: odds and evens; positives and negatives; integers and non-integers; and a very important number, 0.

The moral here: we need to try different kinds of numbers: odds and evens, positives and negatives, integers and non-integers, greater than one and less than one, big numbers and little numbers. Now, for any given problem, some of these categories might be relevant for determining sufficiency, but others won’t. With practice, you’ll be able to identify what issue really matters, and you’ll have a strategic approach to picking numbers.

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Is x negative? (1) x^2 + 25 = 89 (2) x^3 < x

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