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Five friends recently visited a famous chocolatier, and

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by RBBmba@2014 » Thu Apr 09, 2015 11:27 pm
Five friends recently visited a famous chocolatier, and collectively purchased a total of 16 pounds of fudge. Did any one friend purchase more than 5 pounds of fudge?

(1) No two friends purchased the same amount of fudge.

(2) The minimum increment in which the chocolatier sells fudge is one pound.

OA: C

P.S: It took me more than 4 mins to solve it. So,it'd be really great if Experts can provide some smarter and faster solution to this type of problems. Much thanks in advance!
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Source: — Data Sufficiency |
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by GMATGuruNY » Fri Apr 10, 2015 4:16 am
RBBmba@2014 wrote:Five friends recently visited a famous chocolatier, and collectively purchased a total of 16 pounds of fudge. Did any one friend purchase more than 5 pounds of fudge?

(1) No two friends purchased the same amount of fudge.

(2) The minimum increment in which the chocolatier sells fudge is one pound.

Let M = the maximum weight purchased by any of the 5 friends.
Question stem, rephrased:
Is M>5?

Test the THRESHOLD.
Here, the threshold is M=5.
Constraint:
The sum of all 5 weights must be 16 pounds.

Statement 1: No two friends purchased the same amount of fudge.
Case 1: M=5
Here, the other 4 weights must sum to 11.
One option for the other 4 weights: 4, 3, 2.5, 1.5.

Case 2: M=6
Here, the other 4 weights must sum to 10.
One option for the other 4 weights: 5, 4, 1, 0.

Since M=5 in Case 1 but M>5 in Case 2, INSUFFICIENT.

Statement 2: The minimum increment in which the chocolatier sells fudge is one pound.
Case 1: M=5
Here, the other 4 weights must sum to 11.
One option for the other 4 weights: 5, 5, 1, 0.

Case 2: M=6
Here, the other 4 weights must sum to 10.
One option for the other 4 weights: 5, 5, 0, 0.

Since M=5 in Case 1 but M>5 in Case 2, INSUFFICIENT.

Statements combined:
Case 1: M=5
Here, the other 4 weights must sum to 11.
Maximum possible values for the other 4 weights:
4, 3, 2, and 1, yielding a sum of 10.
Doesn't work.

Implication:
For the 5 weights to have a sum of 16, M>5.
SUFFICIENT.

The correct answer is C.
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by RBBmba@2014 » Wed Apr 22, 2015 2:29 am
Thanks GMATGuru. So, is there any smart way to QUICKLY understand where to test such THRESHOLD values ?

Look forward to know your thoughts.
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by [email protected] » Wed Apr 22, 2015 9:58 am
HI RBBmba@2014,

GMAT questions are always carefully worded; the concepts involved are not random and neither are the numbers involved. Noting those details can help you to find those 'pivot points' that you're looking for.

In this prompt, notice how the question focuses on whether any of the friends purchased MORE THAN 5 POUNDS of fudge. That's a rather specific question to ask - noting that, you should be thinking about situations in which someone bought MORE than 5 pounds and situations in which someone bought 5 POUNDS OR LESS.

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by GMATGuruNY » Thu Apr 23, 2015 2:29 am
RBBmba@2014 wrote:Thanks GMATGuru. So, is there any smart way to QUICKLY understand where to test such THRESHOLD values ?

Look forward to know your thoughts.
Some question stems ask for an EXACT VALUE:
How many people attended the party?
Here, the goal is to determine whether we have sufficient information to calculate the exact number of attendees.

Others ask NOT for an exact value but only whether a particular value is beyond a certain THRESHOLD:
Did MORE THAN 10 people attend the party?
Here, it probably will NOT be possible to calculate the exact number of attendees.
But the statements might provide sufficient information to determine whether the number of attendees was BEYOND THE THRESHOLD OF 10.

When a question stem asks not for an exact value but only whether a particular value is beyond a certain THRESHOLD, one approach is to TEST THE THRESHOLD VALUE.
Other threshold problems:
https://www.beatthegmat.com/new-gmatprep ... 13334.html
https://www.beatthegmat.com/weighted-ave ... tml#638076
https://www.beatthegmat.com/need-to-unde ... 65811.html
https://www.beatthegmat.com/how-to-solve-t267385.html
https://www.beatthegmat.com/tough-question-t267902.html
https://www.beatthegmat.com/julie-bought ... 69141.html
https://www.beatthegmat.com/al-s-discoun ... 69537.html
https://www.beatthegmat.com/rates-works- ... 72175.html
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by RBBmba@2014 » Fri Apr 24, 2015 7:37 am
Much thanks GMATGuru for your clarifications and sharing some EXCELLENT problems, especially the 3rd,last and the 1st one in your list.
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