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Desperately need help!!!

by minhngocbui » Wed Jul 09, 2014 9:07 pm
Hello,

Could someone help me to figure out how to recognize GMAT trap from those 2 questions:

OG13-DS9
A citrus fruit grower receives $15 for each crate of oranges shopped and $18 for each crate of grapefruit shipped. How many crates of Orange did the grower shop last week?
(1) Last week the number of crates of oranges that the grower shopped was 20 more than twice the number of crates of grapefruit shipped.
(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped

OG13-DS132
Joana bought only $.15 stamps and $.29 stamps. How many $.15 stamps did she buy?
(1) she bought $4.40 worth of stamps.
(2) she bought and equal number of $.15 stamps and $.29 stamps.

The answer for the first is C. We can somehow guess that at the first sign. However, the second question is A. It has a similar structure to the first one but contains a trap and requires much more work and time. In the test, we could easily make mistake by choosing C (I did).
I am not asking for the questions' solutions, but I would like to know the way to alert such trap so I would not spend much time on an easy question (first one) or blindly guess on a hard question (second one).

Thank you very much!
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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Jul 10, 2014 3:40 am
Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy ?

(1) She bought $4.40 worth of stamps.

(2) She bought an equal number of $0.15 stamps and $0.29 stamps.

Statement 1: She bought $4.40 worth of stamps.
Let $F = the total revenue from the 15¢ stamps and $T = the total revenue from the 29¢ stamps.
Thus:
$F + $T = 440.

This problem is constrained to POSITIVE INTEGERS.
Joanna cannot buy 1/3 of a stamp or -2 stamps.
Whenever a problem is constrained to POSITIVE INTEGERS, be wary:
It is possible that ONE equation will be sufficient to solve for TWO unknowns.

Since the two statements cannot contradict each other, it must be possible in statement 1 that the 440¢ in total revenue is divided according to the ratio indicated in statement 2.
Statement 2 indicates that the ratio of 15¢ stamps to 29¢ stamps = 1:1.
If an equal number of each type of stamp is purchased, we get:
$F : $T = 15:29 = 150:290, for a total of 440¢ in revenue.
Here, the number of 15¢ stamps = 150/15 = 10, and the number of 29¢ stamps = 290/29 = 10.

Check whether OTHER revenue ratios are also possible.
To maintain a sum of 440:
If Joanna buys x¢ LESS of 15¢ stamps, she must buy x¢ MORE of 29¢ stamps.
If Joanna buys x¢ MORE of 15¢ stamps, she must buy x¢ LESS of 29¢ stamps.
Implication:
To change the revenue ratio, the value of x must be a multiple of BOTH 15 and 29..
The LCM of 15 and 29 = 15*29 = 435.
If 435¢ is added to either 150¢ or 290¢, the sum will exceed 440¢.
Thus, the revenue ratio CANNOT be altered, implying that only ONE revenue ratio will satisfy statement 1:
$F = 150¢ and $T = 290¢.
Thus, the number of 15¢ stamps = 10.
SUFFICIENT.

Statement 2: She bought an equal number of $0.15 stamps and $0.29 stamps.
No way to determine how many of each type of stamp were purchased.
INSUFFICIENT.

The correct answer is A.
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by GMATinsight » Fri Jul 11, 2014 8:11 am
Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy ?

(1) She bought $4.40 worth of stamps.

(2) She bought an equal number of $0.15 stamps and $0.29 stamps.
Statement 1)
If X is the No. of Coins $0.15 and Y is the No. of Coins $0.29
Then,
Total Money spent ==> 0.15X + 0.29Y = 4.4

15X + 29Y = 440

There is ONLY ONE INTEGER (because number of Coins has to be Integer) SOLUTION for the equation mentioned above
X=10 and Y=10

Therefore SUFFICIENT

Statement 2)
She bought an equal number of $0.15 stamps and $0.29 stamps
X = Y but the values of X and Y are unknown therefore Insufficient

Answer: Option [spoiler]A[/spoiler]
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by phanikpk » Fri Jul 11, 2014 6:36 pm
OG13-DS132
Joana bought only $.15 stamps and $.29 stamps. How many $.15 stamps did she buy?
(1) she bought $4.40 worth of stamps.
(2) she bought and equal number of $.15 stamps and $.29 stamps.

The answer for the first is C. We can somehow guess that at the first sign. However, the second question is A. It has a similar structure to the first one but contains a trap and requires much more work and time. In the test, we could easily make mistake by choosing C (I did).
I am not asking for the questions' solutions, but I would like to know the way to alert such trap so I would not spend much time on an easy question (first one) or blindly guess on a hard question (second one).

Thank you very much![/quote]

St#1: Total worth= 4.4
0.15x+0.29y=4.4 then the possible values of x and y as integers are 10 and 10 & there will be no other possibility. Because, if we try to change these values then total amount will change.

St#2: Equal number of both the stamps. It can be any integer starting 1 to 100 or 1000 or infinity. So no clear answer.

So, only A
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by GMATinsight » Fri Jul 11, 2014 10:22 pm
A citrus fruit grower receives $15 for each crate of oranges shopped and $18 for each crate of grapefruit shipped. How many crates of Orange did the grower shop last week?
(1) Last week the number of crates of oranges that the grower shopped was 20 more than twice the number of crates of grapefruit shipped.
(2) Last week the grower received a total of $38,700 from the crates of oranges and grapefruit shipped
Assumed,
No. of Crates of Orange = A
No. of Crates of Grapefruit = B

Question: A=?

Statement 1) A = 20+2B

But since B is unknown therefore value of A can't be calculated
INSUFFICIENT

Statement 2) 15A + 18B = 38700 [total amount received as per the respective pricing mentioned]

15A + 18B = 38700 ===> 5A + 6B = 12900

The obtained equation has many solutions
e.g. A = 2580 and B = 0
or A = 2574 and B = 5
or A = 2568 and B = 10

INSUFFICIENT

Combining the Two statements

We get unique values of A and B therefore SUFFICIENT

Answer: Option C
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by GMATinsight » Fri Jul 11, 2014 10:26 pm
The TRAP

Usually many believe that one equation in two variable doesn't lead us to any unique solution However it may give us unique solution several times under given constraints e.g. Integers Non-zero solutions.
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