Company A produced w, x, y and z cars per year respectively over the

Question

Company A produced  w ,  x ,  y  and  z  cars per year respectively over the past four years. If  w < x < y < z , is the median number of cars produced per year less than the mean number of cars produced per year?

(1)  y - x = 48,000

(2)  z - y = x - w

Bunuel · Accepted Answer

GMATNinja Video Solution:

https://www.youtube.com/watch?v=zp4axuvNEcU

percyboi66 · Answer

Could use a check on my solution:

The question stem essentially asks us the question is (x + y)/2 < (x + y + w + z)/4
Which on simplifying gives us: is (x + y) < (w + x + y + z)/2 ------- (1)

S1: y - x = 48000 
which gives us y = 48000 + x

Put this in (1), we get 48000 + 2x < (48000 + 2x + w + z)/2

The most we can simplify this is 48000 + 2x < w + z which does not solve our question

Therefore statement 1 is insufficient

S2: z - y = x - w

this gives us z = x + y - w

Inputting this value in (1) we get (x + y) < (w + x + y + x + y - w)/2

= (x + y) < (2x + 2y)/2
= (x + y) on both sides
Therefore the median = mean which gives us an answer to the question

S2 is sufficient.

Stella5200 · Answer

My logic way of doing this was interpreting as follows:

Question says: Is median less than mean 
My interpretation : is there anyway we can prove this is not an equally spaced set?

1. you cant do much with just (y-x) = 48,000
2. you'll get y-x = z-w. which means the extremes are at the same distance of the 2 years in the middle. so its not an equally spaced set. so 2 is sufficient.

egmat · Answer

Hi percyboi66,

Good news: your solution is correct, and your answer of B is right. Let me confirm each piece and tighten one spot.

Your stem simplification is sound.

The median of four ordered values is the average of the middle two, so median = (x + y)/2, and mean = (w + x + y + z)/4. Asking "is median < mean" is the same as asking "is (x + y)/2 < (w + x + y + z)/4." Clearing the fractions, that reduces all the way to a clean question: is x + y < w + z? Everything you wrote is just a longer-form version of this, so you're on solid ground.

Statement 1 - insufficient (correct).

y - x = 48,000 tells you how far apart the two middle values are, but it says nothing that pins w + z against x + y. Quick two-case check, both obeying w < x < y < z and y - x = 48,000:

- w=1, x=2, y=48002, z=48003 -> x+y = 48004, w+z = 48004 -> equal (median = mean, so "is median < mean?" = No)
- w=1, x=2, y=48002, z=100000 -> x+y = 48004, w+z = 100001 -> x+y < w+z (Yes)

Same statement, two different answers -> not sufficient. Your conclusion is right.

Statement 2 - sufficient (correct).

z - y = x - w rearranges to w + z = x + y. Drop that into the question "is x + y < w + z?" and it becomes "is x + y < x + y?" - which is never true. So the answer is a definite No every time. A definite answer (even a definite "No") is exactly what sufficiency means.

That's the one principle worth locking in: in DS you don't need the answer to be "yes," you just need it to be settled. S2 forces median = mean always, so it settles the question -> sufficient.

Answer: B

percyboi66

Could use a check on my solution:

The question stem essentially asks us the question is (x + y)/2 < (x + y + w + z)/4
Which on simplifying gives us: is (x + y) < (w + x + y + z)/2 ------- (1)

S1: y - x = 48000
which gives us y = 48000 + x

Put this in (1), we get 48000 + 2x < (48000 + 2x + w + z)/2

The most we can simplify this is 48000 + 2x < w + z which does not solve our question

Therefore statement 1 is insufficient

S2: z - y = x - w

this gives us z = x + y - w

Inputting this value in (1) we get (x + y) < (w + x + y + x + y - w)/2

= (x + y) < (2x + 2y)/2
= (x + y) on both sides
Therefore the median = mean which gives us an answer to the question

S2 is sufficient.

Company A produced w, x, y and z cars per year respectively over the

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GMAT Data Sufficiency (DS) Questions

Company A produced w, x, y and z cars per year respectively over the

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards