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by sana.noor » Mon Feb 04, 2013 2:03 am
Sam's grocery store sells potatoes only in 5-pound bags and 10-pound bags. yesterday if the store sold 130 pounds of potatoes, how many 5-pound bags were sold?
1) the number of 5 pound bags sold was 2 more than 4 times the number of 10-pound bags sold
2) the store sold 50 more pounds of potatoes in 5-pound bags than in 10-pound bags.

D
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Source: — Data Sufficiency |
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by hemant_rajput » Mon Feb 04, 2013 3:51 am
sana.noor wrote:Sam's grocery store sells potatoes only in 5-pound bags and 10-pound bags. yesterday if the store sold 130 pounds of potatoes, how many 5-pound bags were sold?
1) the number of 5 pound bags sold was 2 more than 4 times the number of 10-pound bags sold
2) the store sold 50 more pounds of potatoes in 5-pound bags than in 10-pound bags.

D

statement 1:
say, no. of bags of 10 pound of potatoes = x
then no. of bags of 5 pound of potatoes = 4x + 2

so 5(4x+2) + 10 x = 130
after solving x =4
skipping rest of the calculation.

so sufficient.

statement 2

store sold x pound in 10 kg bag and x + 50 in 5 kg bag
say store sold "n" 10 kg bag
this mean store sold 2n + (50/5). [ if sam sold x kg from n 10kg bags , then sam has to sell 2n no of 5 kg to get x kg.]

so now you can use 10 n + 5(2n + 10) = 130

i hope you can do rest of the calculation.
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
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by GMATGuruNY » Mon Feb 04, 2013 4:56 am
sana.noor wrote:Sam's grocery store sells potatoes only in 5-pound bags and 10-pound bags. yesterday if the store sold 130 pounds of potatoes, how many 5-pound bags were sold?
1) the number of 5 pound bags sold was 2 more than 4 times the number of 10-pound bags sold
2) the store sold 50 more pounds of potatoes in 5-pound bags than in 10-pound bags.

D
Let x = the number of 5-pound bags and y = the number of 10-pound bags.
Total weight of the 5-pound bags = 5x.
Total weight of the 10-pound bags = 10y.
Since the total weight of all the bags = 130, we get:
5x + 10y = 130.

Statement 1: The number of 5-pound bags sold (x) was 2 more than 4 times the number of 10-pound bags sold (y).
Since x is 2 more than 4 times y, we get:
x = 2 + 4y.
Since we have two variables (x and y) and two distinct linear equations (5x+10y = 130 and x = 2+4y), we can solve for each variable and determine the number of 5-pound bags.
SUFFICIENT.

Statement 2: The store sold 50 more pounds of potatoes in 5-pound bags than in 10-pound bags.
Since the total weight of the 5-pound bags (5x) is 50 more than the total weight of the 10-pound bags (10y), we get:
5x = 50 + 10y.
Since we have two variables (x and y) and two distinct linear equations (5x+10y = 130 and 5x = 50+10y), we can solve for each variable and determine the number of 5-pound bags.
SUFFICIENT.

The correct answer is D.
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by ceilidh.erickson » Wed Feb 06, 2013 12:05 pm
You don't necessarily have to solve this problem algebraically. When you're two distinct designations of price or quantity, (such as 5-lb and 10-lb bags, $3 and $4 widgets, etc), you know that there are only a limited number of combinations that will add to the given total (in this case, $130). You can quickly write out a chart for all of the possible pairings that will give you that total:
Image

If we want to know how many 5-lb bags there are, we really want to know - can we narrow it down to a single pairing?

1) the number of 5 pound bags sold was 2 more than 4 times the number of 10-pound bags sold
Here, we can intuit that this will only be true for a single pairing. Or we can look at our chart and see where this is true:

Image


2) the store sold 50 more pounds of potatoes in 5-pound bags than in 10-pound bags.
Again, we can intuit that this will only be true for one pairing. Or, we can look at the chart:

Image

In this problem, writing out the chart was somewhat time-consuming, so algebra or intuition might have been more helpful. In other cases, though, if there are only 6 or 7 pairings that work, it can be a quick-n-easy way to approach the problem. And it's always good to have options!
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