Which of the following is closest to 10^180 – 10^30 ?

Question

Which of the following is closest to  10^{180} – 10^{30}  ?

A.  10^{210}

B.  10^{180}

C.  10^{150}

D.  10^{90}

E.  10^6

KarishmaB · Accepted Answer

If you have difficulty in visualizing this approximation, think about it this way:

Which of the following is closest to 10^2 – 10^1 ?

A. 1
B. 10
C. 100
D. 1000

100 - 10 is 90. Since, for a reasonably big number, a smaller power of the number is much smaller than any greater power, the answer will definitely be closer to 10^180 than any other power of 10.

beyondgmatscore · Answer

you can rewrite it as  10^30 *( 10^150  - 1). Now  10^150  - 1 is ~ 10^150  so expression is closest to 10^180.

Answer B

Bunuel · Answer

10^180 is much, much, much bigger number than 10^30 and as we need approximate value then it's pretty much negligible in this case, so: 10^180 – 10^30=~10^180.

Answer: B.

aeglorre · Answer

10^180 - 10^30 can be written as 10^30*(10^150 - 1) just as the first poster said, but one other thing is worth mentioning: PEMDAS.

When you both have multiplication and parenthesis, do the operation in the parenthesis first, then the multiplication. In our case, the subtraction is extremely minescule and thus the parenthesis is almost exactly 10^150.

Now, do the multiplication: 10^30 * 10^150 = 10^180

HKD1710 · Answer

10^180 – 10^30

10^30 * (10^150 – 1)

as we know 10^2 - 1 means 100-1 and we get 99, which is approximately 100. hence (10^150 – 1) would remain as 10^150.
and 10^30 * 10^150 = 10^180. Answer is B.

arvind910619 · Answer

This is a good question for approximation .
 10^180 is much greater than 10^30

Nipungupta9081 · Answer

Answer is B

10^180 - 10^30
taking 10^30 common = 10^30 ( 10^150 - 10^0 )
 = 10^30 ( 10^150 - 1 )
 = 10^30 * 10^150
 = 10^150

Abhishek009 · Answer

10^{180} – 10^{30}

Or,  10^{30}(10^{6} – 10^1)

Or,  10^{30*6} = 10^{180}  (ignoring the value of 10^1, as it is too small in comparison to  10^{180} , Answer must be (B)

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Which of the following is closest to 10^180 – 10^30 ?

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Which of the following is closest to 10^180 – 10^30 ?

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