MGMAT DS

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 391
Joined: Sat Mar 02, 2013 5:13 am
Thanked: 50 times
Followed by:4 members

MGMAT DS

by rakeshd347 » Sun Oct 13, 2013 1:25 am
A list contains twenty integers, not necessarily distinct. Does the list contain at least two consecutive integers?

(1) If any single value in the list is increased by 1, the number of different values in the list does not change.

(2) At least one value occurs more than once in the list.

OA soon.

User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pm
Thanked: 448 times
Followed by:34 members
GMAT Score:650

by theCodeToGMAT » Sun Oct 13, 2013 4:52 am
Is the Answer [spoiler]{A}[/spoiler]?
R A H U L

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Sun Oct 13, 2013 3:17 pm
Hi rakeshd347,

We're told that we have 20 integers (that may or may not include duplicates. We're asked if any two are consecutive? This is a Yes/No question.

Fact 1: If any number is increased by 1, the number of DIFFERENT values DOES NOT CHANGE. This means that changing any of the terms MUST create a new number (and not a number that we already have). By definition, that means that the terms cannot be consecutive.

For example, If we had 20 distinct even values: 2, 4, 6, 8.....40, then increasing any value by 1 will give us the same number of different values (20). The answer to the question is NO.
Fact 1 is SUFFICIENT

Fact 2: At least one value occurs more than once.

This is an easy TEST values situation:

A list with 20 of the same number (for example, all 2s). The answer to the question is NO.
A list with 10 2s and 10 3s. The answer to the question is YES.
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image

Master | Next Rank: 500 Posts
Posts: 269
Joined: Thu Sep 19, 2013 12:46 am
Thanked: 94 times
Followed by:7 members

by mevicks » Sun Oct 13, 2013 7:27 pm
[email protected] wrote:Hi rakeshd347,

We're told that we have 20 integers (that may or may not include duplicates. We're asked if any two are consecutive? This is a Yes/No question.

Fact 1: If any number is increased by 1, the number of DIFFERENT values DOES NOT CHANGE. This means that changing any of the terms MUST create a new number (and not a number that we already have). By definition, that means that the terms cannot be consecutive.

For example, If we had 20 distinct even values: 2, 4, 6, 8.....40, then increasing any value by 1 will give us the same number of different values (20). The answer to the question is NO.
Fact 1 is SUFFICIENT

...
@ Rich, Can't we use the following example to prove St1 INSUFFICIENT:

Let the list contain integers which are very widely spaced after a first few elements.
L = { 1, 3, 3, 9, 100, 200, ... 1600}
No of distinct elements = 18
No of same elements = 2
Constitutive integers = None

St1: Lets increment the first element
L = { 2, 3, 3, 9, 100, 200, ... 1600}
No of distinct elements = 18
No of same elements = 2
Constitutive integers = Yes

Lets increment the last element
L = { 1, 3, 3, 9, 100, 200, ... 1601}
No of distinct elements = 18
No of same elements = 2
Constitutive integers = No

Thus, St1 is INSUFFICIENT

St2: We can use the same list L = { 1, 3, 3, 9, 100, 200, ... 1600} to prove that St2 is INSUFFICIENT.
(Increment the first and the last elements)

St1+St2:
Even after combining the same example can be used to prove that they are INSUFFICIENT together.

[spoiler]IMO Answer : E[/spoiler]

@Rakesh, Nice Share! What is the OA ?

Regards,
Vivek

Master | Next Rank: 500 Posts
Posts: 391
Joined: Sat Mar 02, 2013 5:13 am
Thanked: 50 times
Followed by:4 members

by rakeshd347 » Sun Oct 13, 2013 7:52 pm
rakeshd347 wrote:A list contains twenty integers, not necessarily distinct. Does the list contain at least two consecutive integers?

(1) If any single value in the list is increased by 1, the number of different values in the list does not change.

(2) At least one value occurs more than once in the list.

OA soon.
OA is C Guys all of you got it wrong. This is one of the tough one from MGMAT DS. It is rated 600-700 level from MGMAT. I doubt it if its that level because its very tricky.

Here is the OE from MGMAT.

This problem is annoying because of the number of terms in the list; it's hard to wrap your head around 20 integers. Check the statements to see whether you can think through the problem using a smaller list, or whether it really is necessary to stick with a list of 20. In the case of both statements 1 and 2, the full size of the list doesn't matter; you can think the problem through using an easier list (say, 10 or even 5 numbers) that still represents the basic principles in question.

(1) NOT SUFFICIENT: If the list consists of the numbers 2, 4, 6, 8, 10, then all of the values are different. If any value is increased by 1, the list will still consistent of five different values, so this scenario satisfies the statement. This list does not contain two consecutive integers, so the answer to the question is no.

If, on the other hand, the list consists of four "1"s and a "2", then there are only 2 different values (1 and 2). If any of the 1's is increased, the result is 2, which is already in the list, so there are still two different values. If the 2 is increased, then the list will contain four 1's and a 3, and so the list will still contain only two distinct values. In this case, the original list does contain two consecutive integers (1 and 2), so the answer to the question is yes.

Because there are two conflicting answers to the question (no and yes), this statement is not sufficient.

(2) NOT SUFFICIENT: A list containing four 1's and a 2 contains two consecutive integers (1 and 2). If the list contains four 1's and a 3, then it doesn't contain any consecutive integers. Because there are two conflicting answers to the question, this statement is not sufficient.

(1) AND (2) SUFFICIENT: Statement 2 indicates that at least one value occurs twice; call that value a.

Statement 1 indicates that increasing any value in the list by 1 will not change the number of distinct values in the list. In this case, then, increasing one of the a values by one, to a + 1, will still leave you with a in the list (since there are at least two a values) as well as a + 1. The value of a + 1, then, must already have been in the original list; if it wasn't, then you would have just added a new value without getting rid of an old value, and statement 1 forbids this.

For example, if the original list is {1, 1, 2, 4, 6}, then a = 1 and there are four distinct values in the list. Changing one of the 1's to 2 makes the list {1, 2, 2, 4, 6} and there are still four distinct values. This list does contain two consecutive integers (1 and 2).

If the original list were {1, 1, 3, 5, 7}, then a = 1 and there are four distinct values in the list. Changing one of the 1's to 2 makes the list {1, 2, 3, 5, 7}, but now there are 5 distinct values in the list! This is not allowed, according to statement 1.

As a result, whatever a is, a + 1 must also be in the original list. The original list must contain at least one pair of consecutive integers.

The correct answer is (C).

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Mon Oct 14, 2013 12:12 am
Hi All,

I must admit that I rushed through this question and missed the "exception case" that exists in Fact 1. The idea behind the limitation of the "nineteen 1s, one 2" is what makes Fact 1 INSUFFICIENT and is the only one I can now think of that does.

Mevicks, unfortunately, your second example (the "yes" answer) does NOT fit because if the 2 becomes a 3 then the number of different values changes (and Fact 1 states that the number of distinct values DOES NOT change).

Quite the crafty question. Thankfully, you could get this question wrong and still get an 800 on the GMAT, so it's not the end of the world if any of us were to get it wrong.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image

Master | Next Rank: 500 Posts
Posts: 391
Joined: Sat Mar 02, 2013 5:13 am
Thanked: 50 times
Followed by:4 members

by rakeshd347 » Mon Oct 14, 2013 12:28 am
[email protected] wrote:Hi All,

I must admit that I rushed through this question and missed the "exception case" that exists in Fact 1. The idea behind the limitation of the "nineteen 1s, one 2" is what makes Fact 1 INSUFFICIENT and is the only one I can now think of that does.

Mevicks, unfortunately, your second example (the "yes" answer) does NOT fit because if the 2 becomes a 3 then the number of different values changes (and Fact 1 states that the number of distinct values DOES NOT change).

Quite the crafty question. Thankfully, you could get this question wrong and still get an 800 on the GMAT, so it's not the end of the world if any of us were to get it wrong.

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

I didn't mean to say that way as you took it. I got it wrong too and chose A. But I think this question is bit awkward and that is the reason I mentioned that all got wrong. So I was wondering what would be level of this question. Do you think we are likely to see question like these on GMAT. I mean they are just too absurd.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3380
Joined: Mon Mar 03, 2008 1:20 am
Thanked: 2256 times
Followed by:1535 members
GMAT Score:800

by lunarpower » Mon Oct 14, 2013 2:37 am
Hey, I wrote this problem!
I must admit that I rushed through this question and missed the "exception case" that exists in Fact 1. The idea behind the limitation of the "nineteen 1s, one 2" is what makes Fact 1 INSUFFICIENT.
Yep, that's what I had in mind when I wrote the problem: basically, a smack in the face to those who try to rush through it. Slow down, clarify the goal, and think carefully.

If you consider the whole idea of "increasing by 1 doesn't change the number of values", that means exactly one of two things:
1/ A unique value becomes another unique value;
2/ A duplicate value becomes another duplicate value.
A little bit of thought should reveal that these are the only 2 ways for this to happen. If a previous duplicate becomes a unique value, or vice versa, then the number of different values will change.

It's easy to make a list for statement 1 without consecutive integers (e.g., 2, 4, 6, 8, blah blah blah). As soon as you have that, your only goal in life is to find a list for statement 1 that HAS consecutive integers in it.
Here's the thought process:
* Say you have two consecutive integers (N and N + 1) in the list.
* If you increase N to N + 1, then it's now a duplicate. Therefore, it must have started as a duplicate. So there must be at least two of "N" in the list.
Once you have that, it's not too much of a stretch to think of nineteen N's and one N + 1, or any of many other possibilities that satisfy the constraint.
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

--

Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3380
Joined: Mon Mar 03, 2008 1:20 am
Thanked: 2256 times
Followed by:1535 members
GMAT Score:800

by lunarpower » Mon Oct 14, 2013 2:38 am
and is the only one I can now think of that does
Nah, this isn't the only set that satisfies statement 1 with consecutive integers. There are plenty of others; they just have the feature of having at least two N's and exactly one N + 1, for some "N".

E.g., you could have
nineteen 1's and one 2
nine 1's, a 2, nine 87's, and an 88
1, 1, 1, 2, 4, 4, 4, 5, 7, 7, 7, 8, 10, 10, 10, 11, 13, 13, 13, 14
And so on.
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

--

Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron

Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Sat Dec 07, 2013 7:15 am

by savior » Sat Dec 07, 2013 7:22 am
Hi,

The answer says that C) is correct.

I take statement 1 and statement 2 and it is still possible to find a list that contains two consecutive integers and a list that doesnt as well!

Consider this example:

two consecutive integers:

[1,1,2,4,6]


NOT two consecutive integers:

[2,5,9,11,11]

if i increase 2 by 1, then i have [3,5,9,11,11] which are four different values again! From my point of view, the argument does not say that you can only increase values that occur twice or more often.

Where is my logical gap here?

Can you help me?

Regards,
savior

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3380
Joined: Mon Mar 03, 2008 1:20 am
Thanked: 2256 times
Followed by:1535 members
GMAT Score:800

by lunarpower » Sat Dec 07, 2013 7:28 am
The statement says "If any single value in the list is increased by 1..."
That means the statement has to be true regardless of which value you increase by 1.

In your list (2, 5, 9, 11, 11), the statement works if you increase the 2, the 5, or the 9 by one, but not if you increase one of the 11's. So that list doesn't satisfy the statement.

Just remember, words like "any" are used in exactly the same way as in the real world.
For instance, if someone says "You can ask anyone here and he or she will tell you xxxx", that doesn't mean that there is just one person who will tell you xxxx. It means that absolutely every single person here, if asked, will tell you xxxx.
Same thing with "any single value in the list".
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

--

Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron