Each bead in an urn is marked with a distinct positive integer and col

Question

Each bead in an urn is marked with a distinct positive integer and colored according to that integer’s remainder after division by 5, as shown in the following table:

Remainder Color 
0 ----------- Red
1 ----------- Blue
2 ----------- Green
3 ----------- Yellow
4 ----------- Orange

Four blue beads, three green beads, two yellow beads, and one orange bead are withdrawn. If the product of the numbers on these beads is displayed on another bead, according to the rules above, then the color of that bead is…

(A) red
(B) blue
(C) green
(D) yellow
(E) orange

anudeep133 · Answer

Solution :  Red beads will be of the form 5k, blue - 5k+1 , green - 5k+2 , yellow - 5k+3, orange - 5k+4 .
So, product will be (5k1+1)(5k2+1)(5k3+1)(5k4+1)(5k5+2)(5k6+2)(5k7+2)(5k8+3)(5k9+3)(5k10+4)
Which will effectively be 5(p) + (1)(1)(1)(1)(2)(2)(2)(3)(3)(4) = 5(p) + (1)(8)(9)(4) = 5(p) + 8 = 5(p) + 3. Therefore, Yellow.

Otherwise, just put the values 5 for red, blue - 1 , green - 2 , yellow - 3, orange - 4.
Product = (1)(1)(1)(1)(2)(2)(2)(3)(3)(4) = 288 = remainder 3. Yellow.

Option D.

issamL · Answer

- Bluebead = 5K +1 , so 4*BB = 5*(K*4) + 4 = 5*X + 4 (X=K*4) - Greenbead = 5*V +2 , 3*GB= 5*(3*V) + 6 = 5*(3*V +1) + 1 = 5*Y + 1 Yellow Bead = 5*M+ 3, 2 YB= 5*(2*M) + 6 = 5*(2*M + 1) + 1 = 5*W + 1 ; - 1 Orange bead = 5*Z + 4 ; By multiplying all the terms together, we get as a result a remainder of 1,hence the correct answer is (B).

TheKingInTheNorth · Answer

Each bead in an urn is marked with a distinct positive integer and colored according to that integer’s remainder after division by 5, as shown in the following table:

Remainder Color
0 ----------- Red
1 ----------- Blue
2 ----------- Green
3 ----------- Yellow
4 ----------- Orange

Four blue beads, three green beads, two yellow beads, and one orange bead are withdrawn. If the product of the numbers on these beads is displayed on another bead, according to the rules above, then the color of that bead is…

(A) red
(B) blue
(C) green
(D) yellow
(E) orange

It is a remainder problem : There is simple logic behind the remainder of number when divided by another integer and again using that remainder to get the final . Because from remainder you guess the number ... and thus taking the remainder or number -- will result in the same ans . ( may be my explanation sounds bit odd --- Bunuel hope you got what i am trying to say ... please explain it if possible )

As per the question i will only use the remainder to get the answer to this question .

Four blue beads, three green beads, two yellow beads, and one orange bead are withdrawn.

4 blue = 1*1*1*1
3 green =2*2*2
2 yellow =3*3
1 orange =4

On multiplying the above and dividing by 5 we get our remainder as 3 . Which is yellow .
Hence ans D

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

The key to this problem is to translate the “game” into more familiar mathematical language. First of all, each bead’s color corresponds to a remainder after division by 5. For instance, Red = R0 (remainder of 0), which means that the number in question is a multiple of 5. Blue = R1, Green = R2, etc.

We withdraw four blues, three greens, two yellows, and an orange. In other words, we have four R1 numbers, three R2 numbers, two R3 numbers, and one R4 number.

If we want to, we can pick actual numbers. It would be best to pick small numbers—for instance, R1 could actually be 1, because when you divide 1 by 5, you get a quotient of 0 and a remainder of 1. Likewise, R2 could be 2, R3 could be 3, and R4 could be 4.

Multiplying these numbers together, we get 1x1x1x1x2x2x2x3x3x4 = 8x9x4 = 72×4 = 288. The remainder after division by 5 would be 3, and the color of the bead would be yellow. We would get the same result without picking numbers, of course—we would have to multiply the remainders together, which would give us R288, and then we’d reduce that to R3. Either way, we have a yellow bead.

The correct answer is D.

OC2910 · Answer

SIMPLY 
4 blue beads means =1^4=1
3 green beads means=2^3=8
2 yellow beads means=3^2=9
1 orange beads means=4^1=4
product = 1x8x9x4=288 /5 yields r= 3 therefore yellow ..(D)

chetan2u · Answer

Hi,

The Q says two things--
 1) The number marked on each bead is a distinct positive number and it is not the remainder..
2) the colour on the bead is dependent on the remainder as given in the Q..

Hope it clears the query

bethebest · Answer

Can you please explain how you got the product -> 5(p) + (1)(1)(1)(1)(2)(2)(2)(3)(3)(4) = 5(p) + (1)(8)(9)(4) = 5(p) + 8 = 5(p) + 3 from (5k1+1)(5k2+1)(5k3+1)(5k4+1)(5k5+2)(5k6+2)(5k7+2)(5k8+3)(5k9+3)(5k10+4) Thank you for your help

chetan2u · Answer

Hi,
(5k1+1)(5k2+1)(5k3+1)(5k4+1)(5k5+2)(5k6+2)(5k7+2)(5k8+3)(5k9+3)(5k10+4)..
 when you will open the brackets, all terms will be multiple of 5 apart from the PRODUCT of the terms 1,1,1,1,2,...,4 
example--(5k3+1)(5k4+1)(5k5+2)= 5k3(5k4+1)(5k5+2)+ 1(5k4+1)(5k5+2)= 5k3(5k4+1)(5k5+2)+ 1{5k4(5k5+2)+1(5k5+2)}
=> 5k3(5k4+1)(5k5+2)+ 1*5k4(5k5+2)+1*1(5k5+2) =  5k3(5k4+1)(5k5+2)+ 1*5k4(5k5+2)+1*1*5k5 +1*1*2
 So all terms shown in highlighted portion are multiple of 5.. so 5 is taken out as common and rest are given a variable p.. 
so 5p + 1*1*2.. since we are concerned only about remainders after div by 5
Hope it cleared your doubt

vitaliyGMAT · Answer

\frac{1^4*2^3*3^2*4}{5}

2^2 = 4 = -1(mod 5 ),  3^2 = 9 = -1 (mod 5)

\frac{1*(-1)*2*(-1)*(-1)}{5} = \frac{-2}{5}  = -2 (mod 5)   = 3 (mod 5)

Yellow D .

Sarabjeets746 · Answer

I think we can solve this question a little faster if we don't calculate the product until 288. Instead, since we are dealing with remainders here, I think we only need to concern ourselves with the Units digit - "8". When you divide by 5 any number which ends with 8, you will get 3 as a remainder.

My thought process>>
(1^4∗2^3∗3^2∗4)/5 = (1*8*9*4)/5 => Now multiplying only the units digits
 1*8= 8 (units)
 8*9= 2 (units)
 2*4= 8 (units)
So, in the end we get 8 as units digit and hence, the remainder is 3.  KarishmaB   Bunuel

KarishmaB · Answer

Yes, upon division by 2 or 5 or 10, we need to focus on the units digit only to get the remainder.

samarpan.g28 · Answer

Integers after selection (1,1,1,1),(2,2,2),(3,3),(4). Multiplying we get  1^4 * 2^3 * 3^2 *4=288. Dividing this by 5, we get the remainder as 3. 3 represents the color yellow. Option (D) is correct.

Manifesting710 · Answer

hi  KarishmaB   Bunuel , could you please help me out?

Why are the numbers used in all the answers the same? as in why is it 1,1,1,1,2,2,2,2... or why are we multiplying the remainder? arent we supposed to multiply the integer on the bead?, the question said "Each bead in an urn is marked with a distinct positive integer" so I used the integers for the bead as follows

0, 1, 2, 3, 4,
5, 6, 7, 8, 9,
10, 11, 12, 13, 14
15, 16, 17, 18, 19

4 Blue beads would be 1* 6 * 11 * 16
 (from here i was lost)
3 green beads can be 2*7*12 or any other combination
2 yellow beads can be 3*8 or any other combination
1 yellow bead can be 4 or 9 etc

at this point, i already knew the product is too much and used a calculator to check if I would have got the answer, which upon division by 5 gave a remainder of 2 i.e green

Where did i go so wrong

pappal · Answer

since each of these numbers are divided by 5
hence 1.each of the blue beads should have 6 as the units digit (4 are drawn)=>product still has 6*6*6*6~6 as units digit
2.each of the green beads should have 7 as the units digit (3 are drawn)=>product has 7*7*7~3 as units digit
3.each of the yellow beads should have 8 as the units digit (2 are drawn)=>product has 8*8~4 as units digit
4.each of the orange beads should have 9 as the units digit (1 is drawn)
now each of the above cases are multiplied the units digit of the resultant is 6*3*4*9~ 8 
8 divided by 5 has reminder of 3 hence  yellow  colored.

Wadree · Answer

--------   -----------  
........................... 0 ........................................ red .......................... 5h
........................... 1 ........................................ blue ......................... 5h + 1
........................... 2 ........................................ green ...................... 5h + 2
........................... 3 ........................................ yellow ..................... 5h + 3
........................... 4 ........................................ orange .................... 5h + 4

4 blue....3 green....2 yellow....1 orange.....bead withdrawn.....
Their distinct integer product 
 =   ×   ×  ×   ×   ×   ×   ×   ×  ×   
 =   ] +   
 =   ] + 288 
 =   ] + 285 + 3

So.....only 3 remain.....so.....it will represent bead with 3 remainder ....... Yellow......

!nah id win!

Each bead in an urn is marked with a distinct positive integer and col

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Each bead in an urn is marked with a distinct positive integer and col

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