Hi all,

Can someone please explain to me the logic error I have in the following question?

Of the numbers q, r, s, and t, which is greatest?

(1) The average (arithmetic mean) of q and r is s.

(2) The sum of q and r is t.

Statement 1 alone is insufficent since we do not know the value of t.

Statement 2 alone is insuficient since we do not know the value of s.

Statement 1 & 2 combined: From statement 1 we know that s is the arithmetic mean of q and r, so s falls in between q and r. From statement 2 we know that t is greater than q and r, so by logic deduction we know that t is greater than q, r and s.

So I picked choice C as my answer, but the correct answer is E. Can someone please explain why? Thanks in advance.

rom statement 2 we know that t is greater than q and r[/quote]

q + r = t DOES NOT imply t > q and t > r.
q or r or both can be negative and then t is not the largest amongst the three.

Jameschan,

The best approach in the questions like this is to check the +ve and -ve values both, if you combine both the statements: -

1st Case - assume Q & R be +ve nos

Q = 10
r = 20
So , s = 15
and t = 30 in this case T > r> s > r so, t is the largest

2nd case - assume Q & R be -ve nos

Q = -10
R = -20

So, s = -15 and t = -30 in this case Q > S > R > T, Q is the largest

Hence, insufficient

Hope it helps
GMAT 2007

Thanks GMAT 2007. I seem to still struggle with the DS problems because I have a hard time seeing the "complete picture" if you will. Do you have any tips in a systematic approach to solving DS problems, particuarly number proprerties and inequalities? Thanks is advance.

I follow the following approaches: -

1) Rephrase the question stem first, there is a lot of scope of rephrasing in Number properties and inequalities. It simplifies the problem a little bit.
2) Try to apply mathematical rules, it helps to boil down to the depth of the problem.
3) If I feel (2) is more time consuming or complicated I switch the gears to picking nos. It always helps. But the tricky part in picking nos is to cover all the boundary case like considering +ve or -ve values.

I follow above rules according to my comfortability. I am sure the instructors will have a lot better answer for you.

GMAT 2007

Thanks GMAT 2007.

GMAT 2007's solution and advice are great. The only thing I have to add, in terms of general Data Sufficiency advice, is to

(1) work on the easy statement first

(2) use your grid:

AD
BCE

or

AB
DCE

(3) make sure to keep the information in the two statements separate in your mind, until you have eliminated choices A,B, and D.

-Jad