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15 Feb 2014, 03:29
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
50% (02:38) correct
50%
(02:28)
wrong
based on 519
sessions
History
Date
Time
Result
Not Attempted Yet
A cargo ship carrying four kinds of items, doohickies, geegaws, widgets, and yamyams, arrives at the port. Each item weighs 2, 11, 5, and 7 pounds, respectively, and each item is weighed as it is unloaded. If, in the middle of the unloading process, the product of the individual weights of the unloaded items equals 10,435,040,000 pounds, how many widgets have been unloaded?
A. 2
B. 3
C. 4
D. 625
E. 2,087,008,000
A. 2
B. 3
C. 4
D. 625
E. 2,087,008,000
The OA say we should break the number into primes.. "i'm not sure how to do it with a number this big without taking FOREVER
15 Feb 2014, 03:40
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liranmaymoni
The only thing you are interested is the power of 5 in 10,435,040,000:
\(10,435,040,000=1,043,504*10,000=1,043,504*10,000=1,043,504*(2^4*5^4)\).
Answer: C.
Similar questions to practice:
in-a-certain-game-a-large-container-is-filled-with-red-yel-144902.html (OG PS)
in-a-certain-game-a-large-bag-is-filled-with-blue-green-126425.html (MGMAT PS)
Hope it helps.
General Discussion
15 Feb 2014, 03:36
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Hi liranmaymoni,
you need to know the number of widgets which weight 5 pounds each. This is a very common type of exercise where basically you have a number and need to know how many times a certain prime divides the number.
Here one way to solve the exercise would be to find the full decomposition of the number. This will probably take some time but, however, there is a way to do way faster. You don't need the full decomposition, what you need is just the number of times "5" divides the given huge number which is closely related to the number of times 10 divides the number. Luckily it is really easy to divide a number by 10 !
10,435,040,000= 10,000 * 10,435,04 = 10^4 * 10,435,04 = 5^4 * 2^4 * 10,435,04
Since the last number cannot be divided by 5 (because it does not end either by 0 or 5) you know that the initial number can be divided exactly 4 times by 5 and here comes your answer!
you need to know the number of widgets which weight 5 pounds each. This is a very common type of exercise where basically you have a number and need to know how many times a certain prime divides the number.
Here one way to solve the exercise would be to find the full decomposition of the number. This will probably take some time but, however, there is a way to do way faster. You don't need the full decomposition, what you need is just the number of times "5" divides the given huge number which is closely related to the number of times 10 divides the number. Luckily it is really easy to divide a number by 10 !
10,435,040,000= 10,000 * 10,435,04 = 10^4 * 10,435,04 = 5^4 * 2^4 * 10,435,04
Since the last number cannot be divided by 5 (because it does not end either by 0 or 5) you know that the initial number can be divided exactly 4 times by 5 and here comes your answer!
