If x is a negative integer, which of the following expressions has the

Question

If x is a negative integer, which of the following expressions has the LEAST value?

A.  x^{2} - 0.50 
B.  x^{2} - 0.51 
C.  x^{3} - 0.502 
D.  x^{3} - 0.511 
E.  x^{4} - 0.512

Abhishek009 · Accepted Answer

Take the simples negative integer ( - 1 ) and procceed with the options

A)x^2-0.50

= \((-1)^2\) - 0.50
= 1 - 0.50
= 0.50

B)x^2-0.51

= \((-1)^2\) - 0.51
= 1 - 0.51

From the given options we have 2 negative numbers
= 0.49

C)x^3-0.502

= \((-1)^3\) - 0.502
= - 1 - 0.502
= -1.502

D)x^3-0.511

= \((-1)^3\) - 0.511
= - 1 - 0.511
= -1.511

E)x^4-0.512

\((-1)^4\) - 0.511
= 1 - 0.511
= 0.489

Among the given options we have only 2 negative numbers -

(C) -1.502

(D) -1.511

Now determine the lowest number and mark it as your answer ( If you have any doubt draw a number line )

Attachment:

Numberline.png [ 4.18 KiB | Viewed 40808 times ]

It is clear from the number line that - 1.511 ( option D) is the least possible number , so this is our answer!!

chetan2u · Answer

Hi,
a solution in 20 secs would be..
since it is subtracting something from the power of x, the least would be something with term of x as negative..
x to the power of even number will give positive number and with odd power will give -ive ... so A,B and E can be eliminated..
in D, we are adding a bigger numeric value with a negative sign to another -ive ,x^3..
ans is D

Hope oit helps

BrentGMATPrepNow · Answer

Let x =  -1 , so we get....
A)  ( -1 )^{2} - 0.50  = 1 - 0.50 
B)  ( -1 )^{2} - 0.51  = 1 - 0.51
C)  ( -1 )^{3} - 0.502  = -1 - 0.502
D)  ( -1 )^{3} - 0.511  = -1 - 0.511
E)  ( -1 )^{4} - 0.512  = 1 - 0.512

A, B and E will result in POSITIVE values
C and D will result in NEGATIVE values
Eliminate A, B and E

Answer: D

Cheers,
Brent

EMPOWERgmatRichC · Answer

Hi All,

We're told that X is a NEGATIVE integer. We're asked which of the following expressions has the LEAST value? You can certainly use Number Properties to answer this question. There's also a practical way to get to the correct answer. The question tells us that X is NEGATIVE INTEGER and we're asked which of the 5 answers has the LEAST VALUE. It doesn't ask "which COULD have the least value", it asks "which...HAS.....the least value." So, one of these answer will ALWAYS be smallest whenever X is a NEGATIVE INTEGER. We can TEST VALUES and prove which is smallest.

IF... 
X = -2

A: 4 - 0.50 = +3.5 
B: 4 - 0.51 = +3.49 
C: -8 - 0.502 = -8.502 
D: -8 - 0.511 = -8.511 
E: 16 - 0.512 = +15.488

Answer D is "farther left" on a number line, so it is smaller than Answer C (all of the other answers are positive).

Final Answer:  D

GMAT assassins aren't born, they're made, 
Rich

adkikani · Answer

EMPOWERgmatRichC   Abhishek009   niks18   chetan2u   Bunuel   VeritasPrepKarishma

Why do I require to do  any  sort of calculations? 
I already know that if x is negative, the even powers of 
x will be positive. If I subtract a negative number from a 
positive number instead of subtracting it from a negative number,
the end result will will have higher difference than subtracting a negative
no from a negative number.

Based on this, A, B and E are out.

For C and D, when I subtract a larger negative no from a negative number
(since now power of x is odd) D will have lower value than C.

Let me know if my above approach is correct?

KarishmaB · Answer

Yes, absolutely.

EMPOWERgmatRichC · Answer

Hi adkikani,

Most GMAT questions are designed so that they can be solved in more than one way. Since Number Property rules appear repeatedly in the Quant section, you will have the opportunity to approach a number of different questions in the same general way that you approached this one (re: by knowing the rules and properly interpreting what you're told - and what you're asked to solve for - you can answer the question without doing any calculations at all). That having been said, many Test Takers are more likely to make a mistake when dealing with a concept than when dealing with an actual calculation, so you have to be careful about approaching questions on a conceptual level - you might make a little mistake, not realize it and miss out on some easy points.

GMAT assassins aren't born, they're made,
Rich

ScottTargetTestPrep · Answer

Since x^3 is negative and both x^2 and x^4 are positive, we can narrow down the answer choices to C and D. Since 0.511 is the largest decimal being subtracted from x^3, then x^3 - 0.511, will produce the least value.

Answer: D

CrushTheQuant · Answer

adkikani makes a great point. For some additional thoughts, here's an explanation of this question on YouTube: https://www.youtube.com/watch?v=8WuU0l- ... KjqpAY5r-U

IanStewart · Answer

The exact opposite of this is true, at least when a test taker understands concepts well. With good conceptual understanding, a test taker can avoid a lot of needless calculation, and every calculation a test taker makes is an opportunity to make a careless error. And with that understanding, a test taker can answer many questions more quickly (saving time to double-check work elsewhere in the test, and avoid mistakes on questions that genuinely do require calculation or algebra), and can answer harder questions. Conceptual understanding is really what high-level GMAT questions are testing.

bumpbot · Answer

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If x is a negative integer, which of the following expressions has the

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