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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
In recent a chip can compute 1.026*1015 operations per 1 second. How m  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 51% (03:00) correct 49% (02:39) wrong based on 82 sessions

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In recent a chip can compute $$1.026 \times 10^{15}$$ operations per 1 second. How many hours it took the chip to compute 1 million mega-operations (mega-operations=1 million operations)

A. $$3 \times 10^{-5}$$
B. $$3 \times 10^{-6}$$
C. $$3 \times 10^{-7}$$
D. $$3 \times 10^{-8}$$
E. $$3 \times 10^{-9}$$

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Originally posted by MathRevolution on 10 Jan 2016, 18:36.
Last edited by mikemcgarry on 07 Feb 2017, 12:13, edited 2 times in total.
Reformatted the question to proper mathematical notation.
Math Expert V
Joined: 02 Aug 2009
Posts: 7987
Re: In recent a chip can compute 1.026*1015 operations per 1 second. How m  [#permalink]

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MathRevolution wrote:
In recent a chip can compute 1.026*1015 operations per 1 second. How many hours it took the chip to compute 1 million mega-operations (mega-operations=1 million operations)

A. 3*10-5
B. 3*10-6
C. 3*10-7
D. 3*10-8
E. 3*10-9

*A solution is going to be uploaded in two days.

Hi,
the Q if done the way it is written does not find an answer in the choice...
some Typo error may be...
1 million mega operations= 10^6*10^6=10^12..
1.026*1015 nearly 10^3 operations in 1 sec...
10^3 *3600 in 1 hour..
1 op in 1/(10^3 *3600 )...
10^12 op in 10^12/(10^3 *3600 )...
10^9/3600= nearly 3*10^5...
ans A, if 10-5 was meant to be 10^5....
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: In recent a chip can compute 1.026*1015 operations per 1 second. How m  [#permalink]

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1
How many hours it took the chip to compute 1 million mega-operations (mega-operations=1 million operations)
A. 3*10-5 B. 3*10-6 C. 3*10-7 D. 3*10-8 E. 3*10-9

→ From 1.026*10^16:1 sec=1 million mega-operation:n=10^6*10^6:n, it becomes n=10^12/1.026*10^15 sec. That is, 10^12/1.026*10^15 sec=10^12/(1.026*10^15*3,600)hr=3*10^-7 hr. Therefore, the answer is C.
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Manager  Joined: 09 Jul 2013
Posts: 106
Re: In recent a chip can compute 1.026*1015 operations per 1 second. How m  [#permalink]

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3
MathRevolution wrote:
How many hours it took the chip to compute 1 million mega-operations (mega-operations=1 million operations)
A. 3*10-5 B. 3*10-6 C. 3*10-7 D. 3*10-8 E. 3*10-9

→ From 1.026*10^16:1 sec=1 million mega-operation:n=10^6*10^6:n, it becomes n=10^12/1.026*10^15 sec. That is, 10^12/1.026*10^15 sec=10^12/(1.026*10^15*3,600)hr=3*10^-7 hr. Therefore, the answer is C.

I was about to support and reiterate Chetan4u's solution, but then I figured out where the typo is in the question!

The question is supposed to read:
A new computer chip can compute $$1.026*10^{15}$$ operations per second. How many hours will it take the chip to compute 1 million mega-operations (mega-operations=1 million operations)?

A. $$3*10^{-5}$$
B. $$3*10^{-6}$$
C. $$3*10^{-7}$$
D. $$3*10^{-8}$$
E. $$3*10^{-9}$$

Now we can answer the question the way it was intended.

We are told that a computer chip can perform $$1.026*10^{15}$$ operations per second, and we are asked how many hours it will take for the ship to perform one million million operations ($$10^{12}$$ operations). Since each of the answer choices are separated by a power of 10, then we can safely approximate $$1.026*10^{15} = 1*10^{15}$$.

We can find the number of seconds it will take to perform $$10^{12}$$ operations by dividing the number of operations by the number of operations per second:

$$\frac{12^{12}}{10^{15}} = 10^{-3}$$ seconds.

Now to convert seconds to hours, we need to divide $$10^{-3}$$ seconds by 3600 seconds per hour. Again, since the answer choices are spread out by powers of 10, we can approximate:

$$\frac{10^{-3}}{3.6*10^3} = \frac{10^{-6}}{3.6} ≈ 3*10^{-7}$$

So the answer should be C

Clear notation, like punctuation, makes all the difference...
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Dave de Koos
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Posts: 13316
Re: In recent a chip can compute 1.026*1015 operations per 1 second. How m  [#permalink]

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_________________ Re: In recent a chip can compute 1.026*1015 operations per 1 second. How m   [#permalink] 29 Sep 2018, 11:11
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