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Unsolved problems

by vishal.pathak » Thu Nov 17, 2011 10:32 am
For a certain set of n numbers, where n>1, is the average (arithmetic mean) equal to the median?
(1) If the n number in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2.
(2) The range of the n numbers in the set is 2(n-1).
IMO D, OA A

If t is a positive integer and r is the remainder when t^2+5t+6 is divided by7, what is the value of r?
1) when t is divided by 7 the remainder is 6.
2) when t^2 is divided by 7 the remainder is 1.
Do not have OA

If w, x, y, and z are integers such that w/x and y/z are integers, is w/x + y/z odd?
a. wx + yz = odd
b. wz + xy = odd
Do not have OA
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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Nov 17, 2011 11:57 am
vishal.pathak wrote: If t is a positive integer and r is the remainder when t^2+5t+6 is divided by7, what is the value of r?
1) when t is divided by 7 the remainder is 6.
2) when t^2 is divided by 7 the remainder is 1.
I posted a solution here:

https://www.beatthegmat.com/gmat-prep-2-t90357.html
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by vishal.pathak » Thu Nov 17, 2011 12:03 pm
GMATGuruNY wrote:
vishal.pathak wrote: If t is a positive integer and r is the remainder when t^2+5t+6 is divided by7, what is the value of r?
1) when t is divided by 7 the remainder is 6.
2) when t^2 is divided by 7 the remainder is 1.
I posted a solution here:

https://www.beatthegmat.com/gmat-prep-2-t90357.html
Thanks GMATGuru,

Your explanations always help. Any thoughts on the other 2 questions

Regards,
Vishal
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by GMATGuruNY » Thu Nov 17, 2011 1:25 pm
+
vishal.pathak wrote: If w, x, y, and z are integers such that w/x and y/z are integers, is w/x + y/z odd?
a. wx + yz = odd
b. wz + xy = odd
Before we evaluate the two statements, we should examine how the question stem can be rephrased.

w/x + y/z = (wz + xy)/xz.
Since w/x and y/z are integers, their sum (w/x + y/z) is an integer.
Thus, (wz + xy)/xz must also be an integer.

The question becomes: Is integer w/x + y/z -- which can be rephrased as (wz + xy)/xz -- odd?

Statement 1: wx + yz = odd.
Let w=1, x=1, y=2 and z=2, so that wx + yz = 1*1 + 2*2 = 5.
Is w/x + y/z odd?
NO, since 1/1 + 2/2 = 2.

Let w=1, x=1, y=6, and z=3, so that wx + yz = 1*1 + 6*3 = 19.
Is w/x + y/z odd?
YES, since 1/1 + 6/3 = 3.
INSUFFICIENT.

Statement 2: wz + xy = odd.
Please note the values highlighted in red:
Just as 10/2=5 is a factor of 10, and 12/3=4 is a factor of 12, so too is (wz + xy)/xz a FACTOR of wz + xy.

Since wz + xy is odd, all of its factors must be odd.
Thus, (wz + xy)/xz must be odd.
SUFFICIENT.

The correct answer is B.
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by vishal.pathak » Thu Nov 17, 2011 1:37 pm
GMATGuruNY wrote:+
vishal.pathak wrote: If w, x, y, and z are integers such that w/x and y/z are integers, is w/x + y/z odd?
a. wx + yz = odd
b. wz + xy = odd
Before we evaluate the two statements, we should examine how the question stem can be rephrased.

w/x + y/z = (wz + xy)/xz.
Since w/x and y/z are integers, their sum (w/x + y/z) is an integer.
Thus, (wz + xy)/xz must also be an integer.

The question becomes: Is integer w/x + y/z -- which can be rephrased as (wz + xy)/xz -- odd?

Statement 1: wx + yz = odd.
Let w=1, x=1, y=2 and z=2, so that wx + yz = 1*1 + 2*2 = 5.
Is w/x + y/z odd?
NO, since 1/1 + 2/2 = 2.

Let w=1, x=1, y=6, and z=3, so that wx + yz = 1*1 + 6*3 = 19.
Is w/x + y/z odd?
YES, since 1/1 + 6/3 = 3.
INSUFFICIENT.

Statement 2: wz + xy = odd.
Please note the values highlighted in red:
Just as 10/2=5 is a factor of 10, and 12/3=4 is a factor of 12, so too is (wz + xy)/xz a FACTOR of wz + xy.

Since wz + xy is odd, all of its factors must be odd.
Thus, (wz + xy)/xz must be odd.
SUFFICIENT.

The correct answer is B.
Amazing answer guru, I guess the key was to mould the question in a more useable form

Thanks a lot

Regards,
Vishal
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by GMATGuruNY » Thu Nov 17, 2011 1:38 pm
vishal.pathak wrote:For a certain set of n numbers, where n>1, is the average (arithmetic mean) equal to the median?
(1) If the n numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2.
(2) The range of the n numbers in the set is 2(n-1).
IMO D, OA A
Statement 1: If the n numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2.
In other words, the numbers are EVENLY SPACED.
When numbers are evenly spaced, the average = the median.
SUFFICIENT.

Statement 2: The range of the n numbers in the set is 2(n-1).
If n=2, then the range = 2(2-1) = 2.
Thus, the 2 numbers could be 1 and 3.
Average = (1+3)/2 = 2, median = 2.
Average = median.

If n=3, then the range = 2(3-1) = 4.
Thus, the 3 numbers could be 1,1,5.
Average = (1+1+5)/3 = 7/3, median = 1.
Average ≠ median.
INSUFFICIENT.

The correct answer is A.
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