Saoirse had two purses, each filled with red and white pebbles.

Question

Saoirse had two purses, each filled with red and white pebbles. The first purse had one white pebble for every three red pebbles and the second purse had three white pebbles for every two red pebbles. On Easter, she used all the pebbles in the two purses to create an artwork for her doorstep. The artwork had the same number of red and white pebbles

Select for Purse-I and Purse II, the possible total number of pebbles that Saoirse had in each of her purses respectively, consistent with the information suggested above.
Make only two selections, one in each column

HarshavardhanR · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=83403 Harsha GMAT-Club-Forum-xivg2rry.png

Arsh001 · Answer

Can we do it in multiples, like let us denote white with 'w' and red with 'r'?

So for purse 1, we can denote it in the form w+3r

For purse 2, we can denote it in the form 3w+2r

Now we know that in the final sequence, w=r, so by adding both equations we get 4w+5r.

Now for 4w+ 5r only 1 sequence seems to fit which is 20,50 as any other value will exceed the value in the options available.

agrasan · Answer

Let's say Purse-I has A (white) and 3A (red) marbles
Purse-II has 3B (white) and 2B (red) marbles

We are given that total number of white = total red

A + 3B = 3A + 2B
2A = B

Total Purse-I marbles in single variable = 4A
Total Purse-II marbles in single variable = 5B = 10A

We see ratio is 2:5, only 20 and 50 match from options

Hence, Purse-I is 20 and Purse-II is 50

Adit_ · Answer

Take one of the colors, lets take white:
1/4 is gonna be white in 1st purse
3/5 is gonna be white in second
Final ratio = 1/2 (50-50)
Using mixtures concept and drawing the criss cross:

We get,

3/5-1/2:1/2-1/4 = 1/10:1/4 = 2:5

Therefore,

Answer: 20 in purse 1, 50 in purse 2.

pappal · Answer

purse 1--w:r=1:3 let x and 3x
 and purse 2-- w:r=3:2 let 3y and 2y
given on Easter she has same no. of red and white pebbles when combined together
i.e. x+3y=3x+2y
y=2x
now, in purse 1 total no. of pebbles is a multiple of 4 and in purse 2 is a multiple of 5, 
so in purse1 could be 20=4*5 or 40=4*10 which will correspond to 50=5*10 or 100=5*20 pebbles in purse 2 respectively.
so correct choice is  20,50

SkyBulb · Answer

i get the ratio but is it satisfying condition with x = 20 and y = 50?

Red - 3x + 2y = 60 + 100 = 160
White - x + 3y = 20 + 150 = 170

?

egmat · Answer

Hi SkyBulb,

Great instinct to plug the numbers back in and check! Your equations are exactly the right ones. The only slip is  what 20 and 50 stand for.

Look at the setup others used in the thread: Purse-I is  x  white and  3x  red, so its  total  is  x + 3x = 4x . Purse-II is  3y  white and  2y  red, so its  total  is  3y + 2y = 5y .

So  x  and  y  are the  ratio units ,  not  the purse totals. The options  20  and  50  are the  totals  - the  4x  and  5y , not the  x  and  y .

Convert first, then plug in: 
- Purse-I total =  20 , so  4x = 20  -  x = 5 
- Purse-II total =  50 , so  5y = 50  -  y = 10

Now use  those  values in your own expressions:
- Red =  3x + 2y  =  3(5) + 2(10)  =  15 + 20  =  35 
- White =  x + 3y  =  5 + 3(10)  =  5 + 30  =  35

Red = White =  35 . The condition holds perfectly.

What happened before: you fed the totals ( 20  and  50 ) straight in as  x  and  y , which quietly multiplied every count by  4  and  5 . Once you pull the unit back out first, both columns land together.

So  Purse-I = 20  and  Purse-II = 50  is fully consistent - you just needed the extra step of dividing each total by its ratio-sum ( 4  and  5 ) before substituting.

Answer: Column 1 (Purse-I) = 20; Column 2 (Purse-II) = 50

Saoirse had two purses, each filled with red and white pebbles.

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Saoirse had two purses, each filled with red and white pebbles.

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