Problem Solving

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lucas211: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Mon Aug 04, 2014 5:39 pmFollowed by: 2 members; Thanked: 1 times

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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Source: Beat The GMAT — Problem Solving | Wed Mar 02, 2016 3:53 am

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

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 = 10â�´ 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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Thu Mar 03, 2016 12:49 am

... and what in blazes is a yamyam?

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