Hi
I want to understand the difference between the question no 57 and question number 132 in OG 13 why is the solution given different! Can we solve them with similar methodology?
Thanks
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OG 13 question 57 and 132, similar questions or not?
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OG 57:
Question Stem:
We are looking for the total number of gift certificates sold. We know that more than 5 $50 gift certificates were sold.
1) There are numerous sets of less than 10 $10 gift certificates and more than 5 $50 dollar gift certificates. INSUFFICIENT
2) With only knowledge that there are more than 5 $50 gift certificates there are a number of combinations. Here are just a few:
9 $50 and 1 $10
8 $50 and 6 $10
7 $50 and 11 $10
INSUFFICIENT
Combining the statements, there are still two different ways to satisfy the following conditions.
- More than 5 $50 gift certificates
- Less than 10 $10 gift certificates
- Total value of $460
Here are the examples:
9 $50 and 1 $10
8 $50 and 6 $10
INSUFFICIENT
THE ANSWER IS E
OG 132
Question Stem:
Simply looking for the count of 15 cent stamps
1) The first thing to do if find an example where this will work. Reading between the lines you can see that 15 and 29 add to 44. Thus, if you have 10 of each stamp the total will be $4.40. This is one of the little things you want to start pushing yourself to see. Most often, even though the math may initially look difficult, the GMAT will make calculations simple.
Now that we have one example, we should test for another. In order to find the next value, what you have to look for is the lowest common multiple (LCM) of both 15 and 29. The reason for this is if you add or subtract a certain value from the $0.15 stamps, that exact same value must be replace or add the corresponding value to $0.29 stamps. Since 29 is a prime number, the LCM of the numbers is just the product or $4.35. So, you would have to add $4.35 from the value of $0.15 stamps and add $4.35 to the value of the $0.29 stamps - or vice versa. As you can see from the chart below, this gives you negative values for all other scenarios - something that is not possible in any other scenario. SUFFICIENT
$0.15 $0.29 Total
-$2.85 (-19) $7.25 (25) $4.40
$1.50 (10) $2.90 (10) $4.40
$5.85 (39) -$1.45 (-5) $4.40
Notice that the number of stamps is moving in increments related to the price of the other stamp value.
2) There could be any number of stamps. INSUFFICIENT
THE ANSWER IS A
Question Stem:
We are looking for the total number of gift certificates sold. We know that more than 5 $50 gift certificates were sold.
1) There are numerous sets of less than 10 $10 gift certificates and more than 5 $50 dollar gift certificates. INSUFFICIENT
2) With only knowledge that there are more than 5 $50 gift certificates there are a number of combinations. Here are just a few:
9 $50 and 1 $10
8 $50 and 6 $10
7 $50 and 11 $10
INSUFFICIENT
Combining the statements, there are still two different ways to satisfy the following conditions.
- More than 5 $50 gift certificates
- Less than 10 $10 gift certificates
- Total value of $460
Here are the examples:
9 $50 and 1 $10
8 $50 and 6 $10
INSUFFICIENT
THE ANSWER IS E
OG 132
Question Stem:
Simply looking for the count of 15 cent stamps
1) The first thing to do if find an example where this will work. Reading between the lines you can see that 15 and 29 add to 44. Thus, if you have 10 of each stamp the total will be $4.40. This is one of the little things you want to start pushing yourself to see. Most often, even though the math may initially look difficult, the GMAT will make calculations simple.
Now that we have one example, we should test for another. In order to find the next value, what you have to look for is the lowest common multiple (LCM) of both 15 and 29. The reason for this is if you add or subtract a certain value from the $0.15 stamps, that exact same value must be replace or add the corresponding value to $0.29 stamps. Since 29 is a prime number, the LCM of the numbers is just the product or $4.35. So, you would have to add $4.35 from the value of $0.15 stamps and add $4.35 to the value of the $0.29 stamps - or vice versa. As you can see from the chart below, this gives you negative values for all other scenarios - something that is not possible in any other scenario. SUFFICIENT
$0.15 $0.29 Total
-$2.85 (-19) $7.25 (25) $4.40
$1.50 (10) $2.90 (10) $4.40
$5.85 (39) -$1.45 (-5) $4.40
Notice that the number of stamps is moving in increments related to the price of the other stamp value.
2) There could be any number of stamps. INSUFFICIENT
THE ANSWER IS A
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ceilidh.erickson
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Both of these questions test a similar topic - combinations of 2 items with specific prices: "item X costs $x and item Y costs $y." The solutions are different because, well, the questions are different!
#57 is asking us for the total number of item X's + item Y's. In order to find a total number, we often only need the total cost (if there's only one combination of $x and $y that will get us there). Knowing about on X or only Y won't be sufficient.
(1) If the store sold fewer than 10 $10 certificates, we know nothing about the $50 certificates, and therefor nothing about the total. Insufficient.
(2) If the total cost was $460, ask yourself - is there only one pairing that will bet me this total, or are there multiple?
You can quickly chart out the pairings that will add to $460. There are multiple possible pairings, so this is insufficient.
Now combine the statements to see if it restricts it to a single pairing:
We can see that there are 2 options: 1 $10 and 9 $50, or 6 $10 and 8 $50. Insufficient. The answer is E.
For #132, the question is asking us for the number of a particular item. Once again, it will depend on knowing a total value, and seeing if we can restrict to a single pairing.
(1) If she bought $4.40 worth of stamps, are there multiple pairings that could work? Unlike in the last problem where everything was a multiple of 10, here we have harder-to-work-with numbers. So let's think logically:
- Multiples of the $0.15 stamp will always end in a 0 or a 5. Which multiples of 9, when you add them to 0 or 5, will give you a number that ends in 0? Only $0.29*5, $0.29*10, or $0.29*15 (for products less than $4.40). So you can set up a chart to see if any of these pair with multiples of 0.15:
Here, there's only one pairing of multiples of 0.29 and 0.15 that would work. Sufficient.
(2) Knowing that we have an equal number of each doesn't help if we don't have a total. Insufficient.
The answer is A.
As you can see, we can use the same method of pairings here. But the answers are different because the information given is different!
#57 is asking us for the total number of item X's + item Y's. In order to find a total number, we often only need the total cost (if there's only one combination of $x and $y that will get us there). Knowing about on X or only Y won't be sufficient.
(1) If the store sold fewer than 10 $10 certificates, we know nothing about the $50 certificates, and therefor nothing about the total. Insufficient.
(2) If the total cost was $460, ask yourself - is there only one pairing that will bet me this total, or are there multiple?
You can quickly chart out the pairings that will add to $460. There are multiple possible pairings, so this is insufficient.
Now combine the statements to see if it restricts it to a single pairing:
We can see that there are 2 options: 1 $10 and 9 $50, or 6 $10 and 8 $50. Insufficient. The answer is E.
For #132, the question is asking us for the number of a particular item. Once again, it will depend on knowing a total value, and seeing if we can restrict to a single pairing.
(1) If she bought $4.40 worth of stamps, are there multiple pairings that could work? Unlike in the last problem where everything was a multiple of 10, here we have harder-to-work-with numbers. So let's think logically:
- Multiples of the $0.15 stamp will always end in a 0 or a 5. Which multiples of 9, when you add them to 0 or 5, will give you a number that ends in 0? Only $0.29*5, $0.29*10, or $0.29*15 (for products less than $4.40). So you can set up a chart to see if any of these pair with multiples of 0.15:
Here, there's only one pairing of multiples of 0.29 and 0.15 that would work. Sufficient.
(2) Knowing that we have an equal number of each doesn't help if we don't have a total. Insufficient.
The answer is A.
As you can see, we can use the same method of pairings here. But the answers are different because the information given is different!
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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Tommy Wallach
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Hey Shib,
One last thing: never forget that the actual content tested on the GMAT is quite small (ends at about 8th grade...13 or 14 years old). But because those GMAC folks are cagey, they're able to write thousands upon thousands of different questions. How? Because they explore each little concept in a billion different ways. To that end, make sure you're focusing on mental flexibility, rather than trying to memorize all the different ways that a question can be asked or (even worse) trying to apply one single technique to every question that looks a certain way (i.e. two-variable algebra).
Good luck!
-t
One last thing: never forget that the actual content tested on the GMAT is quite small (ends at about 8th grade...13 or 14 years old). But because those GMAC folks are cagey, they're able to write thousands upon thousands of different questions. How? Because they explore each little concept in a billion different ways. To that end, make sure you're focusing on mental flexibility, rather than trying to memorize all the different ways that a question can be asked or (even worse) trying to apply one single technique to every question that looks a certain way (i.e. two-variable algebra).
Good luck!
-t
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