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# Two bookworms, Alpha and Beta, start eating at opposite ends of a 42

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Intern
Joined: 23 Nov 2010
Posts: 3
Two bookworms, Alpha and Beta, start eating at opposite ends of a 42  [#permalink]

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15 Dec 2010, 21:11
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Difficulty:

85% (hard)

Question Stats:

40% (02:03) correct 60% (02:21) wrong based on 89 sessions

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Two bookworms, Alpha and Beta, start eating at opposite ends of a 42-volume encyclopedia set (numbered 1 to 42), each working directly towards the other. Alpha starts in vol 1 and Beta starts in vol 42. If each volume is the same thickness, where in the set will they be when they meet?

(1) Alpha takes 3 x days to eat through a vol and Beta takes 5 x days, where x > 0.
(2) Alpha eats two volumes more than Beta every 4 days.
Math Expert
Joined: 02 Aug 2009
Posts: 7991
Re: Two bookworms, Alpha and Beta, start eating at opposite ends of a 42  [#permalink]

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27 Jan 2019, 09:10
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mastvita wrote:
Two bookworms, Alpha and Beta, start eating at opposite ends of a 42-volume encyclopedia set (numbered 1 to 42), each working directly towards the other. Alpha starts in vol 1 and Beta starts in vol 42. If each volume is the same thickness, where in the set will they be when they meet?

(1) Alpha takes 3 x days to eat through a vol and Beta takes 5 x days, where x > 0.
(2) Alpha eats two volumes more than Beta every 4 days.

A and B start from two corner towards each other and there are 42 volumes..
(1) Alpha takes 3 x days to eat through a vol and Beta takes 5 x days, where x > 0.
Most important point is that when they meet both have spent equal time
Let A finishes y volume, so B finishes 42-y volume..
Time taken by A = 3x*y=3xy, while time taken by B = 5x*(42-y)..
Thus 3xy=5x(42-y)......3y=210-5y...8y=210...y = 26.25
So B does 42-y=42-26.25
You could also do straight calculations.. work done will be proportionate to their speed..
so speed 3x:5x will mean the work done will be 5:3...
Thus, work done by A = $$42*\frac{5}{8}=\frac{210}{8}=26.25$$
Hence sufficient

Hope it helps
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Kaplan GMAT Instructor
Joined: 21 Jun 2010
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Location: Toronto
Re: Two bookworms, Alpha and Beta, start eating at opposite ends of a 42  [#permalink]

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15 Dec 2010, 21:40
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mastvita wrote:

Q. Two bookworms, Alpha and Beta, start eating at opposite ends of a 42-volume encyclopedia set (numbered 1 to 42), each working directly towards the other. Alpha starts in vol 1 and Beta starts in vol 42. If each volume is the same thickness, where in the set will they be when they meet?
(1) Alpha takes 3 x days to eat through a vol and Beta takes 5 x days, where x > 0.
(2) Alpha eats two volumes more than Beta every 4 days.

Hi!

This is a classic ratio question. Here's the big rule to remember:

if you multiple or divide the parts, you can solve the ratio; if you add or subtract, you can't.

We know the distance travelled before they worms meet (42), so we need either their individual speeds or their relative speeds.

(1) we know their relative rates (a:b = 3x:5x = 3:5), so we can figure out how much each will eat before they meet: sufficient.

(2) with addition or subtraction, you can't figure out the ratio. We can set up:

a:b = 4x+2:4x

but without knowing the value of x, there's no way to figure out where they'll meet.

For example, if worm a eats 2 volumes per day, then in 4 days worm a eats 8 volumes and worm b eats 6 volumes - our ratio is 8:6 = 4:3.

However, if worm a eats 1 volume per day, then in 4 days worm a eats 4 volumes and worm b eats 2 volumes - our ratio is 4:2 = 2:1.

Since we can get different ratios, (2) is insufficient.

(1) is sufficient, (2) isn't: choose (A).
##### General Discussion
Intern
Joined: 23 Nov 2010
Posts: 3
Re: Two bookworms, Alpha and Beta, start eating at opposite ends of a 42  [#permalink]

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16 Dec 2010, 01:43
Manager
Joined: 17 Jun 2018
Posts: 52
Schools: IMD '20
GPA: 2.84
WE: Engineering (Real Estate)
Re: Two bookworms, Alpha and Beta, start eating at opposite ends of a 42  [#permalink]

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27 Jan 2019, 08:52
chetan2u can you explain how 1st statement alone is sufficient?
Manager
Joined: 22 Jun 2017
Posts: 168
Location: Argentina
Schools: HBS, Stanford, Wharton
GMAT 1: 630 Q43 V34
Re: Two bookworms, Alpha and Beta, start eating at opposite ends of a 42  [#permalink]

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22 Feb 2019, 18:10
chetan2u wrote:
mastvita wrote:
Two bookworms, Alpha and Beta, start eating at opposite ends of a 42-volume encyclopedia set (numbered 1 to 42), each working directly towards the other. Alpha starts in vol 1 and Beta starts in vol 42. If each volume is the same thickness, where in the set will they be when they meet?

(1) Alpha takes 3 x days to eat through a vol and Beta takes 5 x days, where x > 0.
(2) Alpha eats two volumes more than Beta every 4 days.

A and B start from two corner towards each other and there are 42 volumes..
(1) Alpha takes 3 x days to eat through a vol and Beta takes 5 x days, where x > 0.
Most important point is that when they meet both have spent equal time
Let A finishes y volume, so B finishes 42-y volume..
Time taken by A = 3x*y=3xy, while time taken by B = 5x*(42-y)..
Thus 3xy=5x(42-y)......3y=210-5y...8y=210...y = 26.25
So B does 42-y=42-26.25
You could also do straight calculations.. work done will be proportionate to their speed..
so speed 3x:5x will mean the work done will be 5:3...
Thus, work done by A = $$42*\frac{5}{8}=\frac{210}{8}=26.25$$
Hence sufficient

Hope it helps

Would you please explain the way the kaplan instructor(Above) solved the problem? Thanks
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Re: Two bookworms, Alpha and Beta, start eating at opposite ends of a 42   [#permalink] 22 Feb 2019, 18:10
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