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# John buys only chocolates and cookies from the market. Was the total

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Math Expert
Joined: 02 Aug 2009
Posts: 5938

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24 Feb 2016, 20:05
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Difficulty:

75% (hard)

Question Stats:

44% (01:19) correct 56% (01:11) wrong based on 144 sessions

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John buys only chocolates and cookies from the market. Was the total money spent by him on cookies and chocolates equal to 375.20?

(1) The cost of one chocolate is 2.25 and one cookie is 1.75.
(2) John puchased 50 chocolates and 100 cookies.

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27 Feb 2016, 00:42
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1

St1: 1 Chocolate = 2.25 and 1 Cookie = 1.75 - Sufficient
The digits after the decimal point for any given number of chocolates can take only the following values: 25, 50, 75, 00
The digits after the decimal point for any given number of cookies can take only the following values: 75, 50, 25, 00
The question asks whether the values after the decimal point in the total cost will be equal to 20? We can clearly see that any addition results in decimal values such as 00, 25, 50 or 75. So we never get the decimal value 20.
St1 is sufficient

St2: Does not give any info on cost - Not sufficient

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27 Feb 2016, 20:50
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1
chetan2u wrote:
John buys only chocolates and cookies from the market. Was the total money spent by him on cookies and chocolates equal to 375.20?
1) The cost of one chocolate is 2.25 and one cookie is 1.75.
2) John puchased 50 chocolates and 100 cookies.

Hi everyone..

the TIMER shows 70% have answered wrongly and 60% have taken C as the answer..
Always remember, DONT FALL FOR TWO VARIABLES AND ONE LINEAR EQUATION IS INSUFF..
check for values. On many occasions, there is a trap waiting for you..

OE

INFO:-

1) only Chocolates and cookies are purchased.
2) is combined cost=375.20

lets see the statements:-

1) The cost of one chocolate is 2.25 and one cookie is 1.75.
let number of chocolates be x and cookies be y..
2.25x + 1.75y = 375.20..
multiply both sides by 100..
225x+175y=37520..
or 25 (9x+7y)= 5(7504)
As we can see the sum of any number of x and y will be a multiple of 25..
But 37520 is not, so 37520 cannot be the answer, irrespective of any value of x and y..
Suff

2) John puchased 50 chocolates and 100 cookies.
although here too the number of choco and cookies are multiple of 50, BUT the cost of each need not be an integer..
so there will be various possiblities for answer to be YES and various other for NO..
Insuff

Ans A

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28 Feb 2016, 18:01
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

John buys only chocolates and cookies from the market. Was the total money spent by him on cookies and chocolates equal to 375.20?

1) The cost of one chocolate is 2.25 and one cookie is 1.75.
2) John purchased 50 chocolates and 100 cookies.

When you modify the original condition and the question, this question is frequently given on GMAT Math, which is "2 by 2" question like the table below.
Attachment:

GCDS chetan2u John buys only chocolates (20160227).jpg [ 18.96 KiB | Viewed 1189 times ]

On the table above, there are 4 variables(a,b,c,d), which should match with the number of equations. So you need 4 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. When 1) & 2), they become 2.25(50)+1.75(100)=287.5, which is no and sufficient. However, this is an integer question, which is one of the key questions and apply the mistake type 4(A).
Then, for 1), 2.25a+1.75b=375.20 -> a=b=positive integer -> Such a and b don’t exist, which is no and sufficient.

 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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24 Aug 2017, 07:04
I didn't do any algebra, i looked at the statement 1 and thought: well it would take me a long time but i bet i can test number to find if the total money for chocolates and cookies could be \$375.20.

Statement 2 is simply not enough because it doesn't give any price of the items.
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GMAT 1: 700 Q50 V34

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31 Oct 2017, 12:11
x - number of cookies, y - no of chocs

Statement 1:
Assume 2.25 x + 1.75 y = 375.2
(9/4) x + (7/4) y = 375.2
9 x + 7 y = (375.2 * 4)
as x, y are integers , LHS will be integer, but RHS (375.2 * 4) wont be integer. So assumpution is false => 2.25 x + 1.75 y != 375.2
Sufficient

Statement 2:
Let a - price of cookie, b - price of choc
50 a + 100 b = 375.2 ? Maybe or maybe not, unlike statement1, a and b need not be integers => Not sufficient

Re: John buys only chocolates and cookies from the market. Was the total   [#permalink] 31 Oct 2017, 12:11
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