parulmahajan89 wrote:The cost of delivery for an order of desk chairs is $10.00 and a charge of $1.00 for any additional chair purchased.If any office manager placed an order of n desk chairs, Is n> 24?

1) The delivery cost for the order total was more than 30.00
2) The average delivery cost per chair of n Chairs was 1.36

Target question: Is n > 24?

Given: The cost of delivery for an order of desk chairs was $10.00 for the 1st chair, and $1 for each additional chair in the order. The office manager placed an order for n desk chairs.

Statement 1: The delivery cost for the order totaled more than $30.00
There are several scenarios that meet this condition. Here are two:
Case a: n = 25, in which case the total cost is $34 (which is more than $30). Here, n is greater than 24.
Case b: n = 23, in which case the total cost is $32 (which is more than $30). Here, n is not greater than 24.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The average (arithmetic mean) delivery cost per chair of the n chairs was $1.36
The average cost of n chairs = (total cost of n chairs)/n
The total cost = $10 for the first chair plus $1 for each of the remaining n-1 chairs
Algebraically, we can say that the total cost = 10 + 1(n-1)
So, the average cost of n chairs = [10 + 1(n-1)]/n
Statement 2 says the average cost is $1.36, so we can write:
[10 + 1(n-1)]/n = 1.36
IMPORTANT: We could solve this equation for n (but we won't), which means we could definitively determine whether or not n > 24.
Since we could answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

parulmahajan89 wrote:
Does plug in number works here? for Statement 2?

Plugging numbers typically works best when you suspect that the statement is not sufficient. In these cases, all you need to do is find values that yield different (conflicting) answers to the target question.

If it turns out that the statement is sufficient, then plugging in values will only give you a general idea of whether or not the statement is sufficient, but you won't be able to make any definitive conclusions.

For example, let's say we have the following target question: Is x > 0?
Let's say statement 1 says: 5x > 4x

Now let's plug in some values of x that satisfy the condition that 5x > 4x.
x = 3, in which case x > 0
x = 0.5, in which case x > 0
x = 15, in which case x > 0
x = 1000, in which case x > 0

So, it APPEARS that statement 1 provides sufficient information to answer the target question. But can we be 100% certain? No. Perhaps we didn't plug in the right numbers. Perhaps there's a number that we could have plugged in such that x < 0

If we want to be 100% certain that a statement is SUFFICIENT, we'll need to use a technique other than plugging in.
Here, we can take 5x > 4x, and subtract 4x from both sides to get x > 0 VOILA - we can now answer the target question with absolute certainty.
So, statement is SUFFICIENT.


To illustrate the potential problems with plugging in, consider this target question: Is positive integer k a prime number?
Statement 1: k is an odd integer.

We should recognize that statement 1 is not sufficient, but notice what happens if we don't choose good numbers to plug in. If x is odd, then here are some possible cases:
x = 3, in which case x is prime
x = 5, in which case x is prime
x = 7, in which case x is prime
Well, I've already plugged in 3 odd integers, and they all led to the same conclusion. So, x must be prime, right? Of course, this is the wrong conclusion.

So, be careful when plugging in values. The only time this technique yields definitive conclusions is when the statement is not sufficient AND you're able to find plug-in values that yield different answers to the target question.

For more information about this important concept, you can watch our free video: https://www.gmatprepnow.com/module/gmat- ... cy?id=1101

Cheers,
Brent

Hi parulmahajan89,

Brent's approach to solving this question is solid, so I won't rehash it here. I will provide some additional insight/tactics into how you might be able to speed up on this question.

Since we're told the price of the chairs ($10 for the first, $1 for each additional) and the question asks if the total NUMBER of chairs is > 24, you can rewrite the question in this way:

24 chairs would cost $10 + 23($1) = $33, so the question is essentially asking: Is the total cost of delivery > $33?

This is what's called "the question behind the question" and it makes dealing with Fact 1 considerably FASTER.

In Fact 2, if you understand how the average formula works, you know that as you increase the number of chairs, the overall average decreases (since each additional chair is only $1). This Number Property means that there's only 1 way to get an average of $1.36, so you don't need to calculate it. With this insight, you wouldn't need to do any math at all to deal with Fact 2.

GMAT assassins aren't born, they're made,
Rich