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Posted on
04
Aug 2021

GMAT Abstract Data Sufficiency Problem

Abstract Data Sufficiency Problems & Scenarios

Hi guys! Abstract data sufficiency problems tend to really lend themselves to running scenarios – It doesn’t matter if it’s an abstract inequality or a number theory problem, really anytime you’ve got variables thrown into the question stimulus on a DS problem, scenarios is a good way to go. Now your scenarios can be discrete actual numbers that you throw in there, but you can also leverage rules and have more conceptual-level scenarios. We’re going to take a look at both in this problem.

Problem Introduction

We’re being asked here for the evenness or oddness of n which is an integer. At first blush, we’re going to say, “Well, if we have the evenness or oddness of any expression involving n and n alone, we should be able to backtrack it to n.” If you don’t see that then you might fall into the trap of having to go much more deeply into it and figure out “Well, what if n is this, what if n is that?” But notice here that because we’re dealing with evens and odds there are a set of identities that govern every possible addition, or multiplication, subtraction, or division of evens and odds. So, as long as there’s nothing complicating it the expression itself will be enough.

Statement 1

Taking a look at the introduced information, number one gives us n2 + 1 is odd that means that n2 is even. How do we know without numbers? If n2 + 1 is odd then adjusting it down by one, removing that one, means we’re definitely going to get to an even, because the number line is just even, odd, even, odd, even, odd all the way up. So, we have n2 is even, and only even times even gives us an even. Odd times odd doesn’t, odd times odd gives us an odd.

So, n must be even if the square of it leads us to an even. Notice again, that we don’t need to do any of that, it’s enough just to say we’ve got n in an expression, and we have its evenness and oddness.

Statement 2

Number two works the same way. 3n + 4 is even that’s enough, no more to do, but if we want to we can adjust that 3n – 4 as even down by 4 notches (odd, even, odd, even). So 3n is even and then we know that n divided by 3, that is what is an even divided by 3, will give us n. An even divided by an odd is going to always be an even, for the same reason even times an odd is always going to be an even.

Run some scenarios here, start out with an even number; let’s do 6, 50, and 120. Divide each by 3; 2 (6/3=2), 50 divided by 3 doesn’t work, 40 (120/3=40). So on the two that do work, we get to even numbers. 50 is not allowed to be used as a scenario because we’re told that n – 3 has to be an integer which means, that 3n must also be an integer; that is 3n is a multiple of 3. Since 50 is not a multiple of 3 it’s not a potential 3n. Take a minute with that one, because it’s kind of looking at everything in reverse.

So here we have two different expressions that both give us evenness and oddness, they both work independently. The answer choice is D – each alone is sufficient.

If you enjoyed this problem, try your hand at these Data Sufficiency Problems GMAT Trade Show Problem & Area of a Triangle Problem.

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Posted on
31
Mar 2021

Ace GMAT Data Sufficiency Questions with this Science Fair Problem

Data Sufficiency Problem Video Transcript

Introduction to Data Sufficiency

Hey guys! Today we’re looking at the Science Fair Problem. In this Data Sufficiency, we’re being asked how many, discrete number, of the 900 students at the school attended all three days. And we can surmise that they’re going to come at us by giving us different breakdowns of how different groups of students behaved and so most likely we’re going to need more than one piece of information to come together in order to give us the precise amount. The only way, typically, that we would have a single piece of information be sufficient is if they gave us the inverse and told us how many, or what percentage, or what fraction of students didn’t attend on all three days. Where we could then compute the opposite.

Statement 1

Let’s take a look: Number 1 is telling us that 30% or 270 of the students attended two or more days. If we break this up into a chart, we see this block that’s undefined but we know that 270 attended either two days or three days. Some mix of them, but we don’t know that mix. Therefore, this doesn’t give us what we need from the box and it’s insufficient. However, we could use it possibly with other information that distinguishes between the two day visitors and the three day visitors.

Statement 2

Number 2 gives us relative information based upon some other number: 10% of those that attended at least one day. That means of all those that attended at all, for one day, for two days, for three days, 10% of those belong in the three-day box. However, we don’t know how many students that is. So 2 is insufficient. When we try and combine them notice that the information from 2 slices and dices a piece of information that 1 doesn’t give us. There’s no way to reconcile the 10% from that big group into the group that just attended two days or three days. Therefore, we don’t have enough information.

Answer

The answer choice is E: both together are still insufficient. Hope this helped. Guys thanks for watching! For other examples of DS problems where you can make charts to fill in the blanks and find the square you need check out the links below and we’ll see you again soon.

If you enjoyed this Data Sufficiency problem video try this Standard Deviation Problem

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