Hard MGMAT question

[pg850]

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?

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OA: 2

[vinayakdl]

IMO : 2

here is the solution:

88000 = (5^3)(2^6)(11)
now since x is greater than 5 and less that 11 we can conclude that x = 2^3 = 8
so

88000 = (5^3)(8^2)(11)

hence 2.

Let me know if this makes sense or i am missing something.

Vinayak

[ManSab]

Vinayak
How you came with 5^3 and 2^6?
88000 = (5^3)(2^6)(11)

Thanks in advance

[vinayakdl]

Vinayak
How you came with 5^3 and 2^6?
88000 = (5^3)(2^6)(11)

Thanks in advance

np...

88000 = 88x1000 = 8x11x10x10x10
= 2^3x11x5x2x5x2x5x2 = 2^6x11x5^3

Vinayak

[ghacker]

the question is about factors

So factorize 88,000

88,000 = 88*1000 = 2^3*11*5^3*2^3 = 2^6*5^3*11

But purple is greater than 5 and less than 11 so it should be 8

Why 8 = 2^3 so 2^6 = 8^2

Hence ans= 2

[pg850]

IMO : 2

here is the solution:

88000 = (5^3)(2^6)(11)
now since x is greater than 5 and less that 11 we can conclude that x = 2^3 = 8
so

88000 = (5^3)(8^2)(11)

hence 2.

Let me know if this makes sense or i am missing something.

Vinayak

Isnt it possible that 88000 blue chips were picked or 8000 red chips were picked. How can we assume that some quantity of each colored chip was picked from the bag, in which case we cannot find out a definite value for x. Maybe I am missing something but I felt the question should have specified these things.

[pg850]

Wait.. I think i figured it out.. "product of the point values" - i.e. even if there were 88,000 blue chips, the product would just be 1.. damn, that was tricky! - need to read the question carefully..

Thanks vinayak!

[kaulnikhil]

y cant we consider 10 as the value of X

we can represent it as
5*(no of green chips = 5*32 )*10*(no of purple chips = 1)* 11 = 8800

so no of purple chips = 1

[tohellandback]

IMO 2
88000=5^3*2^6*11
clearly blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively.

since purple chips are worth more than green chips and less than red chips, purple chips can be worth 6,7,8,9,or 10 points.
88000=5^3*2^6*11- from this we know that there are 3 green chips and 11 red chips.
2^6 represents the purple chips. this can only be written as 8^2. you cannot write it in terms of 6,7,9,or 10. so purple chips are worth 8 points and two of them were selected

[shahdevine]

blue=1
green=5
purple = x
red = 11

we know that red>purple>green, therefore purple's point value is 6,7,8,9, or 10.

since the products of the chips equal 88000 then we can factor 88000 into its primes. We get 5^3*2^6*11. So even although we don't know which chips were picked, based on the prime factors we can figure it out. There were 3 green chips, and 1 red chip. However we have 2^6, is not represented. If we manipulate 2^6 we get 8^2, which means we have a point value for the purple chip which is less than red but greater than green. And we have two purple chips of value 8. Therefore 2 is answer.

blue skies,

sd

[pink_08]

What about the blue chips ??

8 is the point value of the purple chips . Agreed . But there can be 1 purple chip and 8 blue chips .

(i.e ) 2^6 = 2^3 * 2^3 . So 1 purple chip + 8 blue chips.

What in the question gives a hint there are multiple purple chips and 1 blue chip.

[tohellandback]

What about the blue chips ??

8 is the point value of the purple chips . Agreed . But there can be 1 purple chip and 8 blue chips .

(i.e ) 2^6 = 2^3 * 2^3 . So 1 purple chip + 8 blue chips.

What in the question gives a hint there are multiple purple chips and 1 blue chip.

blue chips are worth only 1 point so you can have as many of them as you want..doesn't matter.. but purple chips you can have only 2 because of the 8^2

[pink_08]

Agreed. Blue chips can be as many as needed ( their face value being 1)

What tells that there are 2 purple chips.. 8^2 means you can have even one purple chip and 8 blue chips..What dictates the split of 2 purple

[tohellandback]

Agreed. Blue chips can be as many as needed ( their face value being 1)

What tells that there are 2 purple chips.. 8^2 means you can have even one purple chip and 8 blue chips..What dictates the split of 2 purple

8^2= 8^8. If you have only 1 purple chip then what about the other eight. I think you have mistaken the sum for the product.

8^2 means you can have even one purple chip and 8 blue chips

. those 8 blue chips will give you only one point.

[adssaini]

take a factors of 88,000

its : 11 X 8000

then 8000 = 5 X 1600

16000 = 5 X 320

320 = 5 x 64

64 = 8 X 8

Its given in the question that purple chips are worth more than the green chips, so 8 is higher than 5, and there are two 8's, hence there are 2 purple chips.