In a certain game, a large bag is filled with blue, green, purple and

Question

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?

A. 1
B. 2
C. 3
D. 4
E. 5

A. 1
B. 2
C. 3 
D. 4 
E. 5

The answer is B. I am struggling to understand how. But this is how I am approaching this question. Can someone please help?

Total value of chips = 88,000
Prime factors of 88,000 = 11 * 5^3 * 2^6
Also from question stem = 5<x<11.
We have to find the value of x?
Now, x cannot be 11 because as per question x<11.Now I am struggling after this.

ScottTargetTestPrep · Answer

While your approach is certainly creative, some of the math doesn’t quite work out.

If each purple chip = 10 points, then the product 5 x 2^6 = 5 x 64 = 320.

Now, 10 x 32 = 320 or 10 x 2^5 = 320, so what happened to the factor 2^5? You said it goes to the remaining blue chips. But the blue chips are not 2 points each; the blue chips are only 1 point each. (So the product of the points from the blue chips is always 1^n = 1 for any value of n.) There is no way for the product of the points from blue chips to be 32. (You perhaps overlooked the given information in the question that the blue chips are 1 point each, not 2 points each.)

sanjanam25 · Answer

Why can't we assume purples value as 10? i.e 2*5 then the answer comes up to 3 and not 2

Bunuel · Answer

88,000=2^6*5^3*11=2^3*(2^3*5^3)*11=2^3*(10^3)*11

In this case we cannot accommodate 2^3. Notice that blue, green, and red chips' values are not multiples of 2. So, 2^6 in 88,000 must be the product of the values of the purple chips drawn.

Bhanuodin007 · Answer

i got to the 8x8, meaning two chips, but it doesn't satisfy the 2nd condition of the purple coin worth "The purple chips are worth more than the green chips, but less than the red chips". am i missing something?

16(worth of purple coins)>15(worth of green coins)-- correct
 16(worth of purple coins)<11(worth of red coins) ---   ---- this is the issue

EMPOWERgmatRichC · Answer

Hi Bhanuodin007,

I think that the issue here is how you are interpreting the wording of the prompt. The intended meaning is that A (re: one) purple chip is worth than one green chip and less than one red chip. The reason we can make this particular deduction is that when we factor down 88,000 into its 'pieces', we have just 1 red chip, so neither the TOTAL of the purple chips NOR the TOTAL of the GREEN chips is less than the TOTAL of the red chips - thus, the question cannot be intending for us to deal with the sums of the individual chip colors.

Once you get to the point that you determine that a purple chip is worth 8 points - and there are two of those chips - then you've answered the question.
 
GMAT assassins aren't born, they're made,
Rich

Jaya6 · Answer

I was confused between D and B since 64 is a multiple of both 2 and 4. do we take only prime factors into consideration?

EMPOWERgmatRichC · Answer

Hi Jaya6,

Prime Factorization isn't actually necessary to answer this question - although you will likely need to do some type of 'division' to answer this prompt. Once you 'factor out' the possible 11s and 5s, what's left will account for the product of the value of all the purple chips (you'll find that it's 64). The prompt also tells us the value of a purple chip is greater than 5, but less than 11. I suspect that you probably know many of the standard 'squares' - so it shouldn't be too hard to determine that 64 = 8x8 - and that we have selected 2 purple chips).

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: [email protected]

prateekgupta95 · Answer

Bunuel  I understood your initial explanation but was also wondering why p = 1 cannot work:
1 Purple (1 x 8) = 8
1 Red (1 x 11) = 11
200 Green (200 x 5) = 1,000
Total product value = 88,000

EMPOWERgmatRichC · Answer

Hi prateekgupta95, The prompt tells us that we have to MULTIPLY the value of EACH of the chips together - and the end product will be 88,000. IF.... you had 200 green chips (worth 5 points each), then the value of that piece of the calculation would be 5^200... (NOT 200 x 5). GMAT assassins aren't born, they're made, Rich Contact Rich at: Rich.C@empowergmat.com

VikasBaloni · Answer

I made a mess of this question. For some reason I thought question means that the worth of all the Purple chips picked should be greater than the worth of all the Green chips picked and less than all the Red chips picked. Question never says   each purple chip is   or   a purple chip is worth more than a green chip  .

Is this my weird mind or someone else also thought on similar lines?

Bunuel  - You think my comprehension is way off?

Vanshikakataruka · Answer

I have a general doubt.

why have we taken the equation in powers? 
According to me it should be this: 
1b+5g+xp+11r=88000

Can someone please explain

Bunuel · Answer

Please pay attention to the highlited part in the stem:

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?
 
The question means that (5*5*...)(x*x*...)(11*...) = 88,000

Anshika.g · Answer

@Bunnel If you select 8 Blue chips (each valued at 1), then the answer would change to 1 Purple chip. How can we justify?
Another possibility is if we consider 0 Green and consider the value of purple as 10, then we can have 16 Blue, 1 Red & 3 Purples. 
Thus, I think the question is incorrect and missing details required to provide a single solution.

Bunuel · Answer

The question is precise and correct. The number of blue chips cannot be determined and does not impact the overall calculation, as each blue chip is valued at 1 point. Additionally, each purple chip is specified to be worth more than 5 and less than 11 points.

Here are the point values:
 
Blue = 1 point
Green = 5 points
Purple = x points
Red = 11 points
 
" 0 Green and consider the value of purple as 10, then we can have 16 Blue, 1 Red & 3 Purple" would imply the product of the point values of the selected chips is 1^16 (for Blue) * 11^1 (for Red) * 10^3 (for Purple) = 11,000, not 88,000.

I suggest reviewing the question and the discussion again more carefully.

AnkitNandwani1 · Answer

To determine how many purple chips were selected, we start by analyzing the given conditions and breaking down the product of the point values:

1. **Chip Values**:
 - Blue chips: 1 point
 - Green chips: 5 points
 - Purple chips: $x$ points (where $5 < x < 11$)
 - Red chips: 11 points

2. **Product of Point Values**:
 The product of the point values of the selected chips is 88,000.

We can express 88,000 as a product of its prime factors:
\ 
\ 
\ 
Therefore:
\

3. **Prime Factor Analysis**:
 Each type of chip contributes specific prime factors to the product. Let’s identify the possible factors for each chip:
 - Blue chips (1 point): $1 = 1$ (no contribution to prime factors)
 - Green chips (5 points): $5$
 - Purple chips ($x$ points): $x$
 - Red chips (11 points): $11$

4. **Factor Contribution**:
 We need the factors $2^6$, $5^3$, and $11$.

We know:
- Red chips contribute $11$.
- Green chips contribute $5$.

Let’s see how the chips combine to form $2^6 \times 5^3 \times 11$.

- The 11 must come from exactly one red chip because 11 is a prime number.

Next, we need $x$ to be a factor of 88,000 and fit within the range $5 < x < 11$. Since $x$ is a value between the green and red chips and $5 < x < 11$, the possible value for $x$ that fits between 5 and 11 is $8$.

Thus, $x = 8$ is a valid choice for the purple chips, meaning purple chips are worth 8 points.

5. **Purple Chips Contribution**:
 - Purple chips contribute $2^3$ because $8 = 2^3$.

Putting it together:
\ 
We already have:
- Red chips: 11 (1 chip)
- Green chips: 5 (3 chips)

Thus:
\  comes from:
\ 
So, there must be 2 purple chips contributing $2^3$ each.

Therefore, the number of purple chips selected is:
2

Adarsh_24 · Answer

I think I was the only one confused by the question.

In case some one else finds difficult to understand the question,

1. purple chips are worth more or less -> here they mean each purple chip and NOT the sum of all purple chips in bag. I think wording could have been better to avoid confusion.

2. product of point value -> ok this one is on me. I understand it means if there are 3 red chips(5 point for each). Product of point values will be 5*5*5.

So 88000 = 11 * 2^3 * 10^3 = 11* 2^3 * 2 ^3 * 5^3 = 11 * 2^6 * 5^3

So 11 is a given value => 11*1
5 is given value => 3 of 5 point each
Now remaining 64 which can be 2^6, 4^3, 8^2.
we are given value between 5 and 11. So 8^2.
Answer is 2 since we are asked for number of purple rather than value of purple.

lnyngayan · Answer

Hello Bunuel,

Could you explain more on "The product of the point values of the selected chips is 88,000" this statement?
Is it wrong to write 1B+5G+xP+11R = 88000?
I understand why x is 2^3 but why is the answer 2 purple chips?

Many thanks!

Adarsh_24 · Answer

not bunuel.

but I think you are adding up. 
each point should be multiplied. If you have 5 of 3 points.
it should be 3^5 not 5*3.

Adit_ · Answer

I think that is a good point made for 10.
6 is not possible as there is no 3 as a factor for 88,000.

10 is also NOT possible actually.
Because we need a chip with 5^x. If we use all the power towards 10, like 10^3 then we won't have a 5 as a factor and one chip will be eliminated which we can't do.

But however if we take 10^2 here, then we have an extra 2 left behind, and there are no chips with a 2^x form here.
Thus 10 is also not possible and 8 is the only possibility.

In a certain game, a large bag is filled with blue, green, purple and

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