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08 Feb 2018, 06:35
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A man buys some shirts and some ties. The shirts cost $7 each and the ties cost$3 each. If the man spends exactly $81 and buys the maximum number of shirts possible under these conditions, what is the ratio of shirts to ties? (A) 5:3 (B) 4:3 (C) 5:2 (D) 4:l (E) 3:2 _________________ PS Forum Moderator Joined: 25 Feb 2013 Posts: 1118 Location: India GPA: 3.82 A man buys some shirts and some ties. The shirts cost$7 each and the [#permalink]

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08 Feb 2018, 09:07
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Bunuel wrote:
A man buys some shirts and some ties. The shirts cost $7 each and the ties cost$3 each. If the man spends exactly $81 and buys the maximum number of shirts possible under these conditions, what is the ratio of shirts to ties? (A) 5:3 (B) 4:3 (C) 5:2 (D) 4:l (E) 3:2 Method 1: algebraic let number of shirts be $$x$$ & number of ties be $$y$$ and we need $$\frac{x}{y}$$ i.e. $$x:y$$ so we have $$7x+3y=81$$---------(1) $$3y=81-7x =>y=\frac{(81-7x)}{3} => y= 27-\frac{7x}{3}$$ For $$y$$ to be integer $$x$$ has to be a multiple of $$3$$. so pairs of possible $$x$$ & $$y$$ are (3,20), (6,13), (9,6). Now we need maximum shirt so $$x=9$$ & $$y=6$$ Hence ratio$$=\frac{9}{6}=3:2$$ Option E ---------------------------------------------- Method 2: use substitution. Work through options. For option E: let shirts be $$3x$$ & tie be $$2x$$ so we have $$3x*7+2x*3=81 =>x=3$$ For other options you will not get the common factor as integer, hence can be rejected. Intern Joined: 03 Jul 2015 Posts: 9 Schools: INSEAD Jan '17 Re: A man buys some shirts and some ties. The shirts cost$7 each and the [#permalink]

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08 Feb 2018, 12:23
Bunuel wrote:
A man buys some shirts and some ties. The shirts cost $7 each and the ties cost$3 each. If the man spends exactly $81 and buys the maximum number of shirts possible under these conditions, what is the ratio of shirts to ties? (A) 5:3 (B) 4:3 (C) 5:2 (D) 4:l (E) 3:2 A basic equation can be formed as below...no of shirts be S, no of ties be T 7S+3T=81 => 7S=3(27-T) => 27-T has t be multiple of 7. To maximize S, minimise T , Minimum T cab be 6 so that 27-T ie, 21 is multiple of 7. => S=9 & T=6 => S:T = 3:2 E Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2442 Re: A man buys some shirts and some ties. The shirts cost$7 each and the [#permalink]

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12 Feb 2018, 17:39
Bunuel wrote:
A man buys some shirts and some ties. The shirts cost $7 each and the ties cost$3 each. If the man spends exactly $81 and buys the maximum number of shirts possible under these conditions, what is the ratio of shirts to ties? (A) 5:3 (B) 4:3 (C) 5:2 (D) 4:l (E) 3:2 We can create the equation: 7S + 3T = 81 7S = 81 - 3T 7S = 3(27 - T) S = 3(27 - T)/7 The greatest value of S will be obtained when T is as small as possible. The smallest value of T which produces a number divisible by 7 after substitution is 6, so when T is 6 we have: S = 3(21)/7 = 9 So, the ratio of S to T is 9 : 6 = 3 : 2. Answer: E _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Re: A man buys some shirts and some ties. The shirts cost$7 each and the   [#permalink] 12 Feb 2018, 17:39
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