QES next

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat Feb 21, 2009 5:00 am

The word SQUARE has 6 letters. How many ways can we make QES next to each other and R the third letter?

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Source: Beat The GMAT — Problem Solving | Sat Feb 21, 2009 5:00 am

Alpturk: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sun Feb 15, 2009 12:04 pm

by Alpturk » Sat Feb 21, 2009 4:00 pm

i think that answer must be 1/60

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BuckeyeT: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Sat Jan 24, 2009 3:00 pm; Thanked: 11 times; GMAT Score:730

by BuckeyeT » Sat Feb 21, 2009 4:37 pm

S Q U A R E
Requirements:
(1) R is third letter
(2) QES are next to each other

Since R is the third letter (_ _ R _ _ _), the only way QES can be next to each other are in the final three spots. Otherwise, one is separate from the others (which fails a requirement).

The # of permutations of QES in the final three spots is
3P3 = 3!/0! = 6/1 = 6 permutations.

Since R is constant in the third spot, the final four spots have 6 total permutations.

The first two spots have to contain the unused letters U, A.
2P2 = 2!/0! = 2/1 = 2 (this is just as easily written out)

2 * 6 = 12 ways total.

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tkarthi4u: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Fri Feb 20, 2009 10:38 pm; Thanked: 1 times; GMAT Score:650

by tkarthi4u » Sat Feb 21, 2009 8:46 pm

Hi BuckeyeT,

QES are next to each other but i dont think the order is important.So we will get a seperate 3! words from that combination.Please let me know if i am wrong.

S Q U A R E.

_ _ R (Q E S)

i grouped QES together so QES = x

total no of permutations = 3! * 3! = 36 ways

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Feb 23, 2009 4:55 am

tkarthi4u wrote:Hi BuckeyeT,

QES are next to each other but i dont think the order is important.So we will get a seperate 3! words from that combination.Please let me know if i am wrong.

S Q U A R E.

_ _ R (Q E S)

i grouped QES together so QES = x

total no of permutations = 3! * 3! = 36 ways

nix

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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