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Last month, John had a total of 60 articles- shirts, suits [#permalink]

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01 Oct 2006, 10:29

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Last month, John had a total of 60 articles- shirts, suits or ties- dry cleaned at a cost of $300. If dry cleaning costs $2.00 for each tie, $5.00 for each shirt and $6.50 for each suit, did John have more suits than shirts dry cleaned last month?

(1) John had more than 12 ties dry cleaned last month.
(2) John paid more than $150 to have his suits dry cleaned last month.

Last month, John had a total of 60 articles- shirts, suits or ties- dry cleaned at a cost of $300. If dry cleaning costs $2.00 for each tie, $5.00 for each shirt and $6.50 for each suit, did John have more suits than shirts dry cleaned last month?

(1) John had more than 12 ties dry cleaned last month.
(2) John paid more than $150 to have his suits dry cleaned last month.

THIS IS A BIT LENGHTY( WAY OVER LESS THAN 2 MINUTES
FROM STEM

SH + S + T =60.........ONE
5SH+6.5S+2T = 300 TWO

MUTLIPLU TWO BY 2 AND ONE BY -4 AND ADD TOGETHER

6SH+9S = 360 THUS 2SH+3S = 120.............

FROM ONE

SH+S <=47

ASSUME THAT SH+S = 47 0R 46 OR 45 OR 44......
2SH+3S = 120
SH+S = 47

THUS S=26,SH = 21

IF SH+S = 46 THUS

S = 28 , SH = 19

IF SH+S = 45 THUS

S = 30 AND SH = 17..........ALWAYS S> SH....SUFF

FROM TWO

6.5 S > 150 THUS S > 23

IE COULD BE 24,25,26,27,.............AND IT CAN ONLY BE EVEN NUMBER

SO IT COULD BE (24,26,28,.....)

AND 2SH+3S = 120

THUS SH COULD BE (24 ,.......) THEY COULD BE EQUAL OR NOT

Last month, John had a total of 60 articles- shirts, suits or ties- dry cleaned at a cost of $300. If dry cleaning costs $2.00 for each tie, $5.00 for each shirt and $6.50 for each suit, did John have more suits than shirts dry cleaned last month?

(1) John had more than 12 ties dry cleaned last month. (2) John paid more than $150 to have his suits dry cleaned last month.

Answer C

Smt 1 We can deduce that John had atleast 13 ties . Know nothing about the Shirts and Suits InSuff

Stmt 2 We can deduce John had atleast 24 Suits . Know nothing about Shirts and Ties. InSuff

Combined we have atleast 13 ties and atleast 24 Suits .

So there must me at the most 60 - 13 - 24 = 23 Shirts

Last month, John had a total of 60 articles- shirts, suits or ties- dry cleaned at a cost of $300. If dry cleaning costs $2.00 for each tie, $5.00 for each shirt and $6.50 for each suit, did John have more suits than shirts dry cleaned last month?

(1) John had more than 12 ties dry cleaned last month. (2) John paid more than $150 to have his suits dry cleaned last month.

Answer C

Smt 1 We can deduce that John had atleast 13 ties . Know nothing about the Shirts and Suits InSuff

Stmt 2 We can deduce John had atleast 24 Suits . Know nothing about Shirts and Ties. InSuff

Combined we have atleast 13 ties and atleast 24 Suits .

So there must me at the most 60 - 13 - 24 = 23 Shirts

So we have more Suits than Shirts.

Cool way of solving the problem. C for me too.
_________________

The path is long, but self-surrender makes it short;
the way is difficult, but perfect trust makes it easy.

Last month, John had a total of 60 articles- shirts, suits or ties- dry cleaned at a cost of $300. If dry cleaning costs $2.00 for each tie, $5.00 for each shirt and $6.50 for each suit, did John have more suits than shirts dry cleaned last month?

(1) John had more than 12 ties dry cleaned last month. (2) John paid more than $150 to have his suits dry cleaned last month.

We know that the average cost of each item was $5

Must the number of suits be greater than the number of shirts?
Let's suppose that it is not.

He has had more than 12 ties cleaned, so let 12+k be the number of ties cleaned, where k is a natural number (i.e. positive integer)

Then 48-k is the number of suits and shirts cleaned, at an average price of at most $5.75 (why?)

TOTAL COST is no more than (12+k)*2 + (48-k)*5.75=24+2k+(23*12)-5.75k=300-3.75k<300 since k is a positive integer.

But the total cost is $300, so it must be our supposition is false.

SUFF

(2) He must have had at least 24 suits cleaned 24*13/2=12*13=156. Could he have 24 suits and 24 shirts? This would mean 12 ties. 24(6.50+5)+2(12)= 300. Thus (2) is not sufficient.

Hey kevin, I have neglected the first part of the question ie totally there are 60 items, my god........... i think i should go to my bed............
meet u tomorrow kevin
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