More Primes

[mmukher]

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.

[Stuart@KaplanGMAT]

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.

We know that the purple chips are worth 6, 7, 8, 9 or 10 points each.

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).

[mmukher]

Amazing. Thanks !

[humeixia]

thanks.

[raajan_p]

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.

We know that the purple chips are worth 6, 7, 8, 9 or 10 points each.

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).

Thanks a lot, Stuart!!!

[Thang Do]

I think the short way should be:

As in the context:

(1^a).(5^b).(x^c).(11^d)=88000

a,b,c,d is the numbers of each colour chip.

So we have to find what is c.

To find c we need find x. We will break 88000 in to 1, 5, 11 as follows:

88000 = 88.1000 = 11.8.1000 = 11. 8. 5.5.5.8 = 11.8.8.5.5.5

So

(1^a).(5^b).(x^c).(11^d)=88000 = 5.5.5.8.8.11

Because 1.1.1...1 = 1 so we dont care what is "a".

as we know that 5<x<10 so x= 8 is reasonable.

Thus

5^b = 5.5.5 --->b = 3
x^c= 8^c = 8.8=8^2 ---> c = 2 -----> answer is B
11^d= 11---> d = 1

By this way we can find a,b,c,d

[tanviet]

I can not understand why X can not be 10, Pleas, explain more on this

[mvikred]

The answer is 2.

Can only be 8^2

Cheers !!

[ikaplan]

88000= 88 x 1000

88= 22 x 2 x 2= 11 x 2 x 2 x 2

1000= 10 * 10 * 10= 2^3 x 5^3

so we have:

88000= 11 x 5^3 x 2^6

because (1) "green < purple < red" => 5 < purple < 11 and
because (2) we have @^6 remaining => purple=2^3=8

so there are two purple chips

My answer is B

[pesfunk]

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 ?

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.

We know that the purple chips are worth 6, 7, 8, 9 or 10 points each.

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).

[paritosh_b]

Yes,It's 2.
Good question.

[Stuart@KaplanGMAT]

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 ?

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?

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.

[pesfunk]

Thanks Stuart

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 ?

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?

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.

[anirudhbhalotia]

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.

1. We know that the purple chips are worth 6, 7, 8, 9 or 10 points each.

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).

I couldn't have imagined in my dreams that this is related to Prime nos.! How to make myself acquainted with such problems and how to get the knack of relating the problems to the concepts? I feel like a 6 yr old kid just starting school!

Also for the solution I got till Step 8. But after that I am not able to understand why you did what you did!

Please explain! Thanks!

[kswarna]

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.

We know that the purple chips are worth 6, 7, 8, 9 or 10 points each.


>> 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