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Problem Solving

by lucas211 » Wed Mar 02, 2016 3:53 am
Hello Everybody
Would appreciate some help on the question below.
Thanks in advance

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
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by MartyMurray » Wed Mar 02, 2016 4:40 am
The numbers in the list of weights, 2, 5, 7, and 11, are all prime numbers. So 10,435,040,000 is the product of a unique combination of those numbers raised to certain powers.

Therefore, you could figure out how many items were unloaded by using number properties.

Each widget weighs 5 pounds.

In order to get a 10, you need a 5 and a 2. Also, any number that is a multiple of 5 will end in 5 or 0.

10,435,040,000 = 10,435,04 x 10,000

10,435,04 does not end in 0 or 5. So it is not a multiple of 5.

10,000 = 10� So 10,000 has among its factors four 5's.

So there are 4 5's included in the weights.

Therefore the number of widgets that have been unloaded is 4.

The correct answer is C.
Last edited by MartyMurray on Wed Mar 02, 2016 5:06 am, edited 3 times in total.
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by GMATGuruNY » Wed Mar 02, 2016 4:45 am
lucas211 wrote: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
10,435,040,000 = 1043504 * 10,000 = (non-mulitple of 5) * 10,000 = (non-multiple of 5) * (2*2*2*2) * (5*5*5*5).
The value in red indicates that there are four 5-pound widgets.

The correct answer is C.
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by DavidG@VeritasPrep » Wed Mar 02, 2016 7:36 am
lucas211 wrote:Hello Everybody
Would appreciate some help on the question below.
Thanks in advance

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
For a similar question, see here: https://www.beatthegmat.com/7-5-3-and-2- ... 72667.html
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by Brent@GMATPrepNow » Wed Mar 02, 2016 4:36 pm
lucas211 wrote:
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....
11-pound geegaws? Highly doubtful!!!
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by Matt@VeritasPrep » Thu Mar 03, 2016 12:49 am
... and what in blazes is a yamyam?
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