GRE Question of The Day: Problem Solving

rohit
#1. September 25th, 2006, at 6:17 AM.

Ans is B- 6

raghu kiran
#2. September 25th, 2006, at 1:58 PM.

I got the ans as 5.

Let s1,s2,s3,s4,s5,s6 represent the 6 persons in increasing order of their heights.As desired, assignment of 6 persons in 2 rows can be obtained in following 5 ways:-

1)s4,s5,s6
s1,s2,s3
2)s3,s5,s6
s1,s2,s4
3)s2,s5,s6
s1,s3,s4
4)s3,s4,s6
s1,s2,s5
5)s2,s4,s6
s1,s3,s5
Note that s1 ans s5 needs to be fixed in their alloted positons

akhlesh
#3. September 25th, 2006, at 2:33 PM.

good work raghukiran

imtiaz
#4. September 25th, 2006, at 4:35 PM.

i think its s1 and s6 should be in fixed postions rather than s1 and s6..as said by raghu

imtiaz
#5. September 25th, 2006, at 4:37 PM.

s1 and s6 should be in fixed positins rather than s1 and s5 as said by raghu,…wat do u say raghu>>>

raghu kiran
#6. September 25th, 2006, at 4:38 PM.

Yes,u r right,imtiaz.I have mistakenly typed s6 as s5.

rohit
#7. September 25th, 2006, at 9:46 PM.

ya its A- 5

Saleel
#8. September 26th, 2006, at 10:36 AM.

5

Ashutosh
#9. September 26th, 2006, at 12:20 PM.

Someone plz explain in a better way plz.

varun
#10. October 25th, 2006, at 4:27 PM.

5

Tania
#11. October 26th, 2006, at 12:05 AM.

is there any better way??????? plz??????

Vicky
#12. October 26th, 2006, at 3:40 PM.

the answer is 1.The conditions taken by raghu kiran dont satisfy the 2 conditions mentioned in the questions or kud u please xplain in detail

ylmson
#13. October 15th, 2007, at 12:13 PM.

Method of enumeration:

Assuming the six people are labeled A~F in increasing height order. Let’s make some notation first. We can use “#” to mark people in the first row and “+” to mark people in the second row.

e.g.
###+++: marks a configuration of ABC in the first row, and DEF in the second row. (there is only one configuration since people in each row also stand according to height order)

Obviously, there are same number of #’s and +’s, and we can enumerate all possible combinations using the following constraints: each ‘+’ has to have one corresponding ‘#’ appearing BEFORE it.

The final enumeration for 5 people can thus be systematically obtained in the following way:
ABCDEF
###+++
##+#++
##++#+ (changing the last person in the first row, make first two people A and B)

#+##++
#+#+#+ (make first two people A and C, also change last person)

The answer is 3+2=5. Other configurations are no longer possible. Since A and C being the first two people in the first row are the tallest ones you can put in those positions.

Using similar method, this problem can actually be solved for 8 people of 8 different heights as well. The answer is (4+3+2+3+2) = 14.

Praj
#14. October 15th, 2007, at 10:34 PM.

i came up with 5.
came up with the same method as raghu

zallak
#15. October 17th, 2007, at 5:28 PM.

ans, is D.

Mamta
#16. October 18th, 2007, at 2:22 AM.

Its 5,same as explaind by raghu

zhulander
#17. October 29th, 2007, at 11:11 PM.

Just to clarify using raghu’s terminology, s1 must always be in the lower left corner because it is the lowest possible value, and no value can be placed above it or to its left that is lower.

Same reasoning applies for s6. As the highest possible value, it must go in the upper right corner because no larger value can be placed above it or to its right.

After that, it’s just a matter of plugging in values to go directly above s1. If it is s4:

s4 sX s6
s1 sY sZ

then sX must be s5 to make the top row run lowest to highest, and sY must be s2 and sZ must be s3 for the same reason. This counts as ONE way of arranging.

If it is s3:

s3 sX s6
s1 sY sZ

then sX can be either s4 or s5. sY MUST be s2 in either case, while sZ would be either s5 or s4, respectively. This counts as TWO ways of arranging.

If it is s2:

s2 sX s6
s1 sY sZ

then sX can be either s4 or s5, making sY either s3 or s4, respectively. Note that sX cannot be s3, since that would make it impossible for sY to be a lower value than sX. This counts as TWO ways of arranging.

Adding up all the different ways makes a total of FIVE. So answer A.

anj
#18. October 30th, 2007, at 8:22 PM.

is there no short cut?

polly
#19. October 30th, 2007, at 10:16 PM.

any shoter way to approach this problem ….pls help….

zhulander
#21. October 30th, 2007, at 11:52 PM.

My explanation took a long time to type, but it’s actually pretty simple logic. Shouldn’t take long to think it through in your own mind.

diya
#22. November 1st, 2007, at 2:07 PM.

Ans is 5
just take 6 numbers as 1,2 ,3 ,4 ,5,6,
It will be easier to u to follow the conditions mentioned and get the answer as 5, with actual numbers it is easy and less chance of errors as compared to variables.

meVinay
#23. October 31st, 2008, at 5:53 PM.

Answer is 5
I tried by a simple way …

First row:
1st place - only S1
2nd place - either S2 or S3
3rd place - S4 or S5

second row:
4th place - S2, S3, or S4
5th place - S5 or S4
6th place - S6

We can have 5 combinations of 2nd 3rd 4th and 5th place…
So ……….. ans 5

Garry
#24. October 31st, 2008, at 10:14 PM.

Is this a permutation problem…order of height is important.

6 people…choose 2 or 3?

degange
#25. October 31st, 2008, at 10:16 PM.

i like zhulander’s explanation. that’s the logic i had, too. 5.

Ritz
#26. November 1st, 2008, at 12:36 AM.

1] 4 5 6
1 2 3

2] 3 2 6
1 2 4

3] 3 4 6
1 2 5

4] 2 5 6
1 3 4

5] 2 4 6
1 3 5

Star
#27. November 1st, 2008, at 4:26 AM.

Ans is 36

6 people can be divided into 3 tall and 3 short…
For the first time,
1st row 3C1
2nd row 3C1
that is 3C1*3C1=9
For the second time,
1st row 2C1
2nd row 2C1
that is 2c1*2C1=4
For the third time,
1st row 1C1
2nd row 1C1
that is 1
Therefore 9*4*1=36

correct me if i’m wrong….

Maddy
#28. November 1st, 2008, at 8:43 PM.

I appreciate ylmson’s generalized explanation. Just imagine if u r asked the same problem with 8 ppl. Wouldn’t it be too confusing and time consuming to list down all the possible arrangements.

Anyway, the answer is 5.

sravanthi
#29. November 3rd, 2008, at 10:52 AM.

my ans is 9.
if u select the persons for 1st row it is enough since after this selection ,there is only one way to fill the second row
let us take 123456 are the persons
for 1st place in row1: 1
2nd :2or3or4
3rd :3or4or5
so the probability is 1*3*3=9

junaid
#30. November 6th, 2008, at 5:56 PM.

ans is 5
1 LSP (Lowest significant place) which is left corner of first row.while 6 has to be fixed at MSP(most significant place) right corner of second row.
we have 5 possibilities
456 356 346 256 246
123 124 125 134 135