Three brothersLarry, Garry, and Barryeach spend five hours picking

Question

Three brothers—Larry, Garry, and Barry—each spend five hours picking apples at their own constant rate. Barry picks apples at three times Larry's rate and half of Garry's rate.

In the table, select values for  Garry's rate (apples per hour)  and  Total apples picked by Larry  that are jointly consistent with the information provided. Make only two selections, one in each column.

Bunuel · Accepted Answer

Official Solution:

Assuming Larry's rate is \(x\) apples per hour, Barry's rate will be \(3x\) apples per hour, and Garry's rate will be \(6x\) apples per hour. We need jointly consistent values for Garry's rate (apples per hour), \(6x\), and Total apples picked by Larry, which in 5 hours would be \(5x\) apples. Thus, the ratio of the value in the left column to the value in the right column must be 6 to 5. Only 78 and 65 satisfy this condition.

Correct answer:

Garry's rate (apples per hour) "78"

Total apples picked by Larry "65"

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Attachment:

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Bismuth83 · Answer

1. Let Larry, Garry, and Barry have rates L, G, and B.

2. It is known that B = 3L and 2B = G. That means 6L = G.

3. Let the total number of apples picked by Larry be x. Since they were picking apples over 5 hours, then x = 5L or L =  \frac{x}{5} .

4. We are given no further information and need to find x and G. So, let's look at the ratio:  6 * \frac{x}{5} = G \rightarrow \frac{x}{G} = \frac{5}{6} .

5. The only options that fit this ratio are 65 and 78 ( \frac{65}{78} = \frac{13 * 5}{13 * 6} = \frac{5}{6} = \frac{x}{G} ).

6. So, our answer is:   Garry's rate - 78 and Total apples picked by Larry - 65  .

silviao · Answer

when you say Only 78 and 65 satisfy this condition how would you do the math quickly to solve which numbers work for the answer?

Bunuel · Answer

Here the fastest approach is just trial and error. Since the ratio must be 6:5, test likely pairs from the list. Only 78 and 65 fit, because 78:65 = 6:5.

egmat · Answer

Hi silviao,

Great question — here's the fast way to crack this.

First,  set up the key relationship. Let Larry's rate = L.

- Barry's rate =  3 L (three times Larry's)
- Barry's rate = G/ 2  (half of Garry's), so G =  2  ×  3 L =  6 L

This gives you the   golden ratio: Garry's rate is always  6  times Larry's rate.

Now, since Larry picks for  5  hours, Larry's total =  5 L, which means Larry's rate = Larry's total ÷  5 .

Substitute that into the golden ratio:

Garry's rate =  6  × (Larry's total ÷  5 ) = ( 6 / 5 ) × Larry's total

So the quick test is: Garry's rate must be exactly  6/5  of Larry's total. That's the only thing you need to check.

Now scan the answer choices  —  6 ,  13 ,  52 ,  65 ,  78 ,  390  — and ask: which pair has a  6 -to- 5  ratio?

-  78  and  65  →  78  ÷  65  =  6/5   ✓

No other pair works. Try a few to confirm:
-  390  and  65  →  390 / 65  =  6  ( too big )
-  78  and  52  →  78 / 52  =  3/2  ( wrong ratio )
-  52  and  13  →  52 / 13  =  4  ( nope )

Only  78  and  65  have that  6 -to- 5  relationship.

So Garry's rate =  78  apples per hour, and Larry's total =  65  apples.

To verify:  Larry's rate =  65  ÷  5  =  13 . Barry's rate =  3  ×  13  =  39 . Garry's rate =  2  ×  39  =  78 .  Everything checks out.

Speed trick:  derive the ratio between the two columns (here,  6/5 ), then scan for the pair of numbers with that ratio. That way you avoid testing every combination.

Answer: 5A, 4B

Three brothersLarry, Garry, and Barryeach spend five hours picking

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Garry's rate (apples per hour)	Total apples picked by Larry
		6
		13
		52
		65
		78
		390

GMAT Two-part Analysis (TPA) Questions

Three brothersLarry, Garry, and Barryeach spend five hours picking

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