Set J consists of terms {2, 7, 12, 17, a}. Is a > 7? (1) a is the

VERITAS PREP OFFICIAL SOLUTION:

For most, statement 1 looks very sufficient, as if a is the “middle number” then it would go between 7 and 12 on the list {2, 7, a, 12, 17}. That would mean that on this chart, you’re at A, as statement 2 is pretty worthless on its own:

___D___

A_____B

___C___

___E___

You can very confidently eliminate B and probably E, too, but if you’re sitting on a “probable A,” you’ll want to consider one level above and one level below your answer on the chart. Why? Because if the answer is, indeed, trickier than your first-30-seconds-assessment, the options are that either:

*The statement you thought was sufficient was close, but there’s a little hiccup (you thought A, but it’s C)

*The statement you thought was not sufficient was actually really cleverly sufficient had you just worked a little harder to reveal it (you thought A, but it’s D)

This is what Veritas Prep’s Data Sufficiency book calls “The Reward System” – many questions are created to reward those examinees who dig deeper on an “obvious” answer via critical thinking, and to “punish” those who leap to judgement and fall for the sucker choice. If A is the sucker choice, the answer is almost always D or C, so you know what you have to do…check to make sure that statement 2 is not sufficient, and then check (often using statement 2) to make sure that you haven’t overlooked a unique situation that would show that statement 1 is actually not sufficient. And here, further review shows this:

If a = 7, a is still the median of the set, but 7 is NOT greater than 7, so that answer would be “no” – there’s a way that a is not greater than 7, so we actually need statement 2. If there is no mode, then a can’t be 7 (that would be a duplicate number, making 7 the mode). So the answer is C, and the Reward System thinking can help make sure you streamline your thought process to help you identify that. If you picked A you’re not alone – many do. But if you picked A and then considered the chart:

___D___

A_____B

___C___

___E___

You should have spent that extra 30 seconds making sure that the answer wasn’t C or D, and that may have given you the opportunity to reap the rewards of thinking critically via the Data Sufficiency question structure.

So remember – merely knowing what the answer choices are is an elementary step in Data Sufficiency mastery; learning to use those to your advantage via the Reward System will help you avoid trap answers and stake your place among those being rewarded.

This is one of those quant questions for which you don't need to write on scrap paper but just think critically, click the answer and move on. Doing such questions would also help get away with bad habbit of directly jumping on solving the question.

stmt-1: If a is the median of set J, then it can be anything from 7 to 12, inclusive. so this a=7 or a>7. insuff.

stmt-2: Right away looking at B sees that it helps stmt-1 to be sufficient because it removes a=7 as a possibility because if there is no mode, it means no number in the set can repeat. But be aware to always check the sufficiency of a stmt alone itself whenever that stmt make the other sufficient. this helps get away C-Trap.
obviously a can be any number different from those given in set j. hence insufficient.

Answer is C.

1. a is a median , so A can be equal to or greater than 7 ..so insuff
2. A can be 1 ,3 11 etc ..so in suff

combining 1 and 2 we will get a cant be equal to 7 ...only values a can have is greater than 7.
C

Hi there ,

I am little bit confused , as per my understanding the answer should be A because a “SET”always consists of DISTINCT terms .

Either a set could be Null which consists of zero terms or it could be a normal set which consists of different terms .

Bunuel VeritasKarishma and all other experts , kindly guide

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But as per my understanding , a set can never contain repetitive terms

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Hi Bunuel ,

Why we are considering a set with duplicate terms here ?

Didn’t understand this

Plz help

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Concept:

Mean is average of sets.
Median is the central element of the set if arranged in ascending order. (For even number of elements, mean of two central elements upon arrangement)
Mode: Element with the highest frequency of occurrence.

To find if a>7 (Stem)

Statement#1

For a to be the median a can be 7 (Stem No)
a can also be 7.1 (Stem Yes) Insufficient

Statement#2

a can't be 2, 7, 12, 17. But anything apart from theses. Insufficient

1+2 Together says us that a has to be >7 and !=(2, 7, 12, 17) (Stem Yes)

C

This is not true.

Please refer to the GMAT Club Math-book: https://gmatclub.com/forum/gmat-math-book-87417.html

Thanks Leo for the kind gesture , but I am unable to download the book ?

Could you let me know whether you are able to download the pdf formatted book or not

Check the attachment please.

Hi LeoN88

I am able to download the pdf now .
Thank you so so so much for sharing this useful pdf with me , I understand my mistake regarding the SET and am going through other topics as well.

Now I am clear , a set can contain anything (any Element ), unless and until specified explicitly .

Once again thankuuuu

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Set j: 2, 7, 12, 17, a
Is a>7?

Statement 1: a= median
2, 7, a, 12, 17
a can be 7 or greater than 7
Insufficient
Statement 2:
Set j has no mode
No number is repeated in set j
a can be anything
Insufficient
Both statements together
a is median and set j has no mode
a can only be greater than 7
Sufficient
C

Hello Leena,

In Math, a set is defined as a collection of WELL DEFINED terms and NOT DISTINCT terms (well, not necessarily). You seem to have gotten these two mixed up in your head.

For example, can we have a set of numbers representing the temperature of a city on a given set of days, say? You will respond in the positive to my question.
1) Why? Because, the numbers representing the temperatures are well defined.
2) Does that mean that the temperature cannot be same on two consecutive days? It can be, right?
3) If two temperatures are same, can you NOT record one of them because they are same numbers? No, you can’t do that either because you’re recording temperatures and missing out numbers would tantamount to providing faulty data for analysis.

On the other hand, can we make a set of good tennis players? Absolutely not! Because an entity like “Good tennis player” is not well defined. X may be a great tennis player in your opinion whereas I may see him as the WOAT (antonym of GOAT which is the acronym for Greatest Of All Time).

Summarising, “A set is a collection of WELL DEFINED objects/terms” and not necessarily distinct terms. I hope that this has resolved the confusion in your mind about the actual question and that you will be able to appreciate the solution given by the various experts.

Thanks!

Whaoooo ,

What an explanation sir
Now it’s pretty clear

Thankuuuu

That's not true. A set in math is a collection of distinct objects. So, a set, strictly speaking, cannot have repeated terms. Usually GMAT uses "data set" or "list" instead, whcih could have repeated terms. So, yes, the question should have used one of those the solution provided to be correct.

Will edit.

Hi Bunuel ,

If thats the case then my understanding of Set was correct !

Infact I looked the question stating “Set J consists ......, and thought that the answer should be A “

So , the question should explicitly state “ Data set J consists of ..... or List J consists of terms ....“ — this is what you mean to say ?

Yes. GMAT is not making questions on technicalities of various definitions. So, to avoid this, they will most likely use "list" or "data set" or say "set of measurements" instead of "set".