If x = 10^10, (x^2 + 2x + 7)(3x^2 - 10x + 2) is closest to

Question

If  x = 10^{10} ,  \frac{x^2 + 2x + 7}{3x^2 - 10x + 200}  is closest to:

A.  \frac{1}{6} 
B.  \frac{1}{3} 
C.  \frac{2}{5} 
D.  \frac{1}{2} 
E.  \frac{2}{3}

m19 q30

Bunuel · Accepted Answer

\frac{x^2 + 2x + 7}{3x^2 - 10x + 200}=\frac{10^{20} + 2*10^{10} + 7}{3*10^{20} - 10*10^{10} + 200} . Note that we need approximate value of the given expression. Now, since 10^{20} is much larger number than 2*10^{10} + 7 , then 2*10^{10} + 7 is pretty much negligible in this case. Similarly 3*10^{20} is much larger number than -10*10^{10} + 200 , so -10*10^{10} + 200 is also negligible in this case. So, \frac{10^{20} + 2*10^{10} + 7}{3*10^{20} - 10*10^{10} + 200} \approx {\frac{10^{20}}{3*10^{20}} =\frac{1}{3} . Answer: B. Similar questions to practice: https://gmatclub.com/forum/which-of-the ... 10224.html https://gmatclub.com/forum/the-value-of ... 95082.html https://gmatclub.com/forum/tough-and-tr ... l#p1029229 Hope it helps.

sje12 · Answer

I'm not sure which book it is from, however I obtained it from a course instructor in Switzerland (Absolute GMAT, gmat-kurse.ch)

EMPOWERgmatRichC · Answer

Hi All,

The phrasing in this question ("is closest to") is meant to hint that we can avoid an exact calculation.

From the answer choices, we can see that the denominator is going to be bigger than the numerator, so we have to think about how those two values really relate to one another....

Since X = 10^10, we know that we're dealing with a BIG number

The numerator gives us X^2 and the denominator gives us 3(X^2)

(10^10)^2 = 10^20 which is A LOT BIGGER than 10^10

Here they are, for context:

10^10 = 10,000,000,000
10^20 = 100,000,000,000,000,000,000
3(10^20) = 300,000,000,000,000,000,000

10^20 and 3(10^20) are so much bigger than the other "elements" in the numerator and denominator that those other elements are "negligible" (by comparison) to the overall calculation.

This means that we're basically dealing with (X^2 + a little)/(3X^2 - a little). That fraction is approximately 1/3

Final Answer:  B

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

seed · Answer

I solved it incorrect with timer but without i did it as below:

- We know that  10^{10}  is a large number so, ignored 7 and 200 from numerator and denominator.
- Now the expression becomes  \frac{X(X+2)}{X(3X-10)} . Cancel out X, left with  \frac{X+2}{3X-10} .
- Apply same logic  10^{10}  is huge, ignored 2 and -10 so eventually the expression becomes  \frac{1}{3}  after cancelling X again. So, Option (B).

rahul16singh28 · Answer

This problem can best be solved by taking  x^2  as common in numerator and  3x^2  in denominator. As  x  is a large number.. anything divided by  x  or  x^2  will be almost negligible provided numerator is also smaller.

JeffTargetTestPrep · Answer

Plugging 10^10 for x we have:

10^20 + 2(10^10) + 7 for the numerator

3(10^20) - 10(10^10) + 200 for the denominator

Since 10^20 and 3(10^20) are such large values compared to the other terms, we see that the approximate value of the expression is:

10^20/3(10^20) = 1/3

Answer: B

Kinshook · Answer

Asked: If  x = 10^{10} ,  \frac{x^2 + 2x + 7}{3x^2 - 10x + 200}  is closest to:

\frac{x^2 + 2x + 7}{3x^2 - 10x + 200} = \frac{10^20 }{ 3* 10^20} = \frac{1}{3}

IMO B

naikabhishekjanu · Answer

Hi Bunuel,

Is there any way for us to determine when we need to use approximation to answer the question and when we need to solve the equation given and then find the answer. It's just I spend time too much time solving the equation and then see you have used approximation to get to the answer which is way easier and timesaving in some situation

If x = 10^10, (x^2 + 2x + 7)(3x^2 - 10x + 2) is closest to

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If x = 10^10, (x^2 + 2x + 7)(3x^2 - 10x + 2) is closest to

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