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We know that the purple chips are worth 6, 7, 8, 9 or 10 points each.mmukher wrote:In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 88,000, how many purple chips were selected?
Options :
1
2
3
4
5
OA later.
Thanks a lot, Stuart!!!Stuart Kovinsky wrote:We know that the purple chips are worth 6, 7, 8, 9 or 10 points each.mmukher wrote:In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 88,000, how many purple chips were selected?
Options :
1
2
3
4
5
OA later.
The blue chips are worth 1 point each, so we can ignore those.
Let's break 88000 down to primes:
88 * 1000
11 * 8 * 10 * 10 * 10
11 * 2 * 2 * 2 * 2 * 5 * 2 * 5 * 2 * 5
so:
2^6 * 5^3 * 11
Well, we're not getting any 2s out of the 1, 5 or 11, so all the 2s have to come from x.
Therefore, x has to be 6, 8 or 10.
x can't be 6, because we don't want any 3s.
If x were 10, it would give us 2s and 5s. So to get 6 2s we'd also have to take 6 5s, which is way more than we want.
Therefore, x MUST be 8.
To get 2^6, we need two 8s: choose (b).
Stuart Kovinsky wrote:We know that the purple chips are worth 6, 7, 8, 9 or 10 points each.mmukher wrote:In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 88,000, how many purple chips were selected?
Options :
1
2
3
4
5
OA later.
The blue chips are worth 1 point each, so we can ignore those.
Let's break 88000 down to primes:
88 * 1000
11 * 8 * 10 * 10 * 10
11 * 2 * 2 * 2 * 2 * 5 * 2 * 5 * 2 * 5
so:
2^6 * 5^3 * 11
Well, we're not getting any 2s out of the 1, 5 or 11, so all the 2s have to come from x.
Therefore, x has to be 6, 8 or 10.
x can't be 6, because we don't want any 3s.
If x were 10, it would give us 2s and 5s. So to get 6 2s we'd also have to take 6 5s, which is way more than we want.
Therefore, x MUST be 8.
To get 2^6, we need two 8s: choose (b).
Well, you could pose the same question about a lot of the topics covered by the GMAT. How often do you think an MBA grad needs to solve a quadratic equation or find the sum of a sequence?pesfunk wrote:Great question and awesome explanation...but Stuart, can this be a GMAT question...i mean the methods used....why would GMAT test this for an MBA ?
Stuart Kovinsky wrote:Well, you could pose the same question about a lot of the topics covered by the GMAT. How often do you think an MBA grad needs to solve a quadratic equation or find the sum of a sequence?pesfunk wrote:Great question and awesome explanation...but Stuart, can this be a GMAT question...i mean the methods used....why would GMAT test this for an MBA ?
Prime numbers (and number properties in general) are consistently tested on the GMAT, so this is definitely a possible GMAT question (and a very high level one, at that).
Here's the thing to remember: even though there's a lot of math on the GMAT, what you're really being tested on is your critical thinking and strategic problem solving skills - things every MBA applies on a daily basis. That's why you'll almost never see a question such as "what are the prime factors of 88,000?"; instead, you'll see a complicated word problem that forces you to apply that information in an unexpected context.
Stuart Kovinsky wrote:1. We know that the purple chips are worth 6, 7, 8, 9 or 10 points each.mmukher wrote:In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 88,000, how many purple chips were selected?
Options :
1
2
3
4
5
OA later.
2. The blue chips are worth 1 point each, so we can ignore those.
3. Let's break 88000 down to primes:
4. 88 * 1000
5. 11 * 8 * 10 * 10 * 10
6. 11 * 2 * 2 * 2 * 2 * 5 * 2 * 5 * 2 * 5
7. so:
8. 2^6 * 5^3 * 11
9. Well, we're not getting any 2s out of the 1, 5 or 11, so all the 2s have to come from x.
10. Therefore, x has to be 6, 8 or 10.
11. x can't be 6, because we don't want any 3s.
12. If x were 10, it would give us 2s and 5s. So to get 6 2s we'd also have to take 6 5s, which is way more than we want.
13. Therefore, x MUST be 8.
14. To get 2^6, we need two 8s: choose (b).
Stuart Kovinsky wrote:We know that the purple chips are worth 6, 7, 8, 9 or 10 points each.mmukher wrote:In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 88,000, how many purple chips were selected?
Options :
1
2
3
4
5
OA later.
>> IT IS NOT GIVEN ANYWHERE THAT IT NEEDS TO BE IN ORDER. X CAN BE 2,3,4 TOO as purple has a value in between the highest and lowest values. This can be either the specified 5 or this can be the unspecified x. So the answer should be right applied to either. now
88,000 = 11 * 8000 *1
= 11 * (20)^3 * 1
= 11 * ( 4 * 5 ) ^ 3 *1
I.E the answer is 3 CHOICE C
