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Data sufficiency

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by DavidG@VeritasPrep » Wed Mar 08, 2017 10:19 am
How many odd integers are greater than the integer x and less than the integer y?
1) There are 12 even integers greater than x and less than y
2) There are 24 integers greater than x and less than y
Statement 1: There are 12 even integers greater than x and less than y

Case 1: x = 1 and y = 25. Number of odds greater than 1 and less than 25 = 11 (All the odds between 3 and 23 inclusive)
Case 2: x = 1 and y = 26. (Notice there are still 12 even numbers that are greater than 1 and less than 26.) Number of odds greater than 1 and less than 26 = 12. (all the odds between 3 and 25 inclusive.)

Because we can get different results - there could be 11 or 12 odds greater than x and less than y - statement 1 is not sufficient.


Statement 2: There are 24 integers greater than x and less than y. We can use Case 2 again here: x = 1 and y = 26. (There are 24 integers between 2 and 25 inclusive.) We already know there are 12 odds between 1 and 26.

What if x = 2 and y = 27? The number of odds greater than 2 and less than 27 = 12. (All the odds from 3 to 25 inclusive.) No matter what we pick, there will always be exactly 12 odds greater than x and less than y. We have a single unique value. This statement alone is sufficient. The answer is B
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by [email protected] » Wed Mar 08, 2017 3:38 pm
Hi Arun6765,

In these types of situations, it can sometimes be helpful to try 'locking in' certain variables, so that you can "play around" with other variables (and see what happens).

This question tells us that X and Y are integers. It essentially asks us for the number of ODD integers between X and Y (but not counting X or Y).

1) There are 12 EVEN integers greater than X and less than Y

Let's try 'locking in' 12 consecutive even integers....
2 4 6 8 10
12 14 16 18 20
22 24

With this list of 12 even integers...
X COULD be 0 or 1
Y COULD be 25 or 26

How do those options effect the question that is asked?
IF... X=0, Y=26, then the answer to the question is 13
IF... X=1, Y=25, then the answer to the question is 11
Fact 1 is INSUFFICIENT

2) There are 24 integers greater than x and less than y

This Fact doesn't describe the integers as 'odd' or 'even', so we're just dealing with 24 consecutive integers. Since we know that X and Y are integers, by definition - half of those 24 integers will be odd and half will be even.

As an example, let's "lock in" the integers 1 through 24... In this scenario
X MUST be 0
Y MUST be 25
The answer to the question is 12.

If we increase or decrease X, then we have to also increase or decrease Y by the same value - but this won't change the number of odd or even integers. Thus, the answer to the question will ALWAYS be 12.
Fact 2 is SUFFICIENT

Final Answer: B

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by Matt@VeritasPrep » Wed Mar 15, 2017 4:47 pm
You can also make this one a little easier by trying smaller numbers. (Since we're dealing with odds and evens here, 12 and 24 are arbitrary numbers: we can find the pattern by replacing them with smaller evens, such as 2 and 4.)
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by aalobaidy » Wed Apr 26, 2017 12:44 am
[email protected] wrote:Hi Arun6765,

In these types of situations, it can sometimes be helpful to try 'locking in' certain variables, so that you can "play around" with other variables (and see what happens).

This question tells us that X and Y are integers. It essentially asks us for the number of ODD integers between X and Y (but not counting X or Y).

1) There are 12 EVEN integers greater than X and less than Y

Let's try 'locking in' 12 consecutive even integers....
2 4 6 8 10
12 14 16 18 20
22 24

With this list of 12 even integers...
X COULD be 0 or 1
Y COULD be 25 or 26

How do those options effect the question that is asked?
IF... X=0, Y=26, then the answer to the question is 13
IF... X=1, Y=25, then the answer to the question is 11
Fact 1 is INSUFFICIENT

2) There are 24 integers greater than x and less than y

This Fact doesn't describe the integers as 'odd' or 'even', so we're just dealing with 24 consecutive integers. Since we know that X and Y are integers, by definition - half of those 24 integers will be odd and half will be even.

As an example, let's "lock in" the integers 1 through 24... In this scenario
X MUST be 0
Y MUST be 25
The answer to the question is 12.

If we increase or decrease X, then we have to also increase or decrease Y by the same value - but this won't change the number of odd or even integers. Thus, the answer to the question will ALWAYS be 12.
Fact 2 is SUFFICIENT

Final Answer: B

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

In answering that question. Reading information B, (There are 24 integers greater than x and less than y), how could you know that there are ONLY 24 integers between x and y. To be honest, my answer for this question was non of the two statements is sufficient to answer the question.
Let me explain my problem;
X=1 and y=1000000 truly has 24 integers larger than x and smaller than y.
My wife says i am confused cuz am over complicating things.
Please advise.
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by [email protected] » Wed Apr 26, 2017 1:48 pm
Hi aalobaidy,

Each of the two statements are essentially 'Facts' that you have to incorporate into how you solve the prompt - and you MUST follow that information. Here, Fact 2 tells us that there are 24 integers between X and Y - no more, no less (and you should not overthink that information). When including that Fact, X=1 and Y=1,000,000 is NOT a possibility, since there are 999,998 integers between those two values - and that result does NOT match what you were told.

No GMAT questions are ever trying to 'trick' you. Data Sufficiency questions ARE designed to test you in a variety of ways though, including the 'thoroughness' of your thinking (as you probably noticed in Fact 1).

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by aalobaidy » Wed Apr 26, 2017 8:50 pm
[email protected] wrote:Hi aalobaidy,

Each of the two statements are essentially 'Facts' that you have to incorporate into how you solve the prompt - and you MUST follow that information. Here, Fact 2 tells us that there are 24 integers between X and Y - no more, no less (and you should not overthink that information). When including that Fact, X=1 and Y=1,000,000 is NOT a possibility, since there are 999,998 integers between those two values - and that result does NOT match what you were told.

No GMAT questions are ever trying to 'trick' you. Data Sufficiency questions ARE designed to test you in a variety of ways though, including the 'thoroughness' of your thinking (as you probably noticed in Fact 1).

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

Hello Rich,

That was crystal clear.

Thank you,
Ahmad
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by Matt@VeritasPrep » Thu May 11, 2017 8:06 pm
aalobaidy wrote: Let me explain my problem;
X=1 and y=1000000 truly has 24 integers larger than x and smaller than y.
My wife says i am confused cuz am over complicating things.
Please advise.
This is a great question, and one that comes down to everyday English. When we give a number with no other qualifications, such as "I have two cats", we assume that that number is correct and complete to the best of the speaker's knowledge. When we somehow qualify the number ("I have two cats that like to go outside"), however, all bets are off: I could have other cats that like to stay inside.
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by Matt@VeritasPrep » Thu May 11, 2017 8:07 pm
[email protected] wrote:Fact 2 tells us that there are 24 integers between X and Y - no more, no less (and you should not overthink that information).
(bolds mine) ... except it does not explicitly say that, it implicitly does, and it relies on English usage to do so, which is something worth elaborating.
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