Given the ascending set of positive integers {a, b, c, d, e,

[Guest]

MGMAT Gurus-

I have a question on MGMAT CAT 1: Question: "Does my Middle Look Big" in Quant section.

"Given the ascending set of positive integers {a, b, c, d, e, f}, is the median greater than the mean?

(1) a + e = (3/4)(c + d)

(2) b + f = (4/3)(c + d)"

I got the answer as C, however, I have a question on the given solution:

Is 2c + 2d > a + b + e + f ?
Is 2(c + d) > (3/4)(c + d) + (4/3)(c + d)?
Is 2(c + d) > (25/24)(c + d)?
Now, we can divide by c + d, a quantity we know to be positive, so the direction of the inequality symbol does not change.
Is 2 > 25/24 ? <----Is this a typo? If you divide both sides by 2, aren't you left with 1>25/24?

[GMAT 5/18]

Guest,

To answer your question you typed in bold, you do not get 1>25/24. Instead, you get 1>25/48.

This is because 25/24 divided by 2 is the same as 25/24 multiplied by 1/2 (the reciprocal of 2). Remember, the reciprocal of a number can be found by:
Y x reciprocal = 1 (basically, a number multipled by its reciprocal will equal 1).

Dividing a fraction (numerator) by a number or another fraction (denominator) is easiest solved by multiplying the numberator with the reciprocal of the denominator.

Thus, 25/24 x 1/2 = 25/48, which is less than 1.

Hope that helps!

[Guest]

Thanks GMAT 5/18--but I was quoting the exact solution from MGMAT.

If you start from the second line of the solution, you'll see:

Is 2(c + d) > (3/4)(c + d) + (4/3)(c + d)? ->2(c+d)>25/12(c+d)-->(c+d)>(25/12 * 1/2)(c+d)
After dividing both sides by (c+d), result is: 1>25/24

Just wanted to check with MGMAT staff if this is an error in the solution or if I'm just not getting it.

thanks.

[Guest]

How do we know that this is the inequality that we want to work with in the first place: Is 2c + 2d > a + b + e + f ?

Thanks!

[Guest]

Guest- This inequality can be gleaned by rephrasing:

Question: Is the median greater than the mean? or
Is median (c+d)/2 > average (a+b+c+d+e+f)/6

6(c+d)>2(a+b+c+d+e+f)
3c-c+3d-d>(a+b+e+f)
Rephrased question is: Is 2c+2d > a+b+e+f?

[esledge]

To the original poster with the question about the typo:

I believe that is/was a typo. As written:
"Is 2(c + d) > (3/4)(c + d) + (4/3)(c + d)?
Is 2(c + d) > (25/24)(c + d)? <---The error happened here, when we summed 3/4 and 4/3; should be 25/12

Now, we can divide by c + d, a quantity we know to be positive, so the direction of the inequality symbol does not change.
Is 2 > 25/24 ?" <--should be "Is 2 > 25/12?" (alternatively, "Is 1 > 25/24?")

Thanks for pointing it out; it will be fixed.