Mashika: We already know from polling data that some segments of the e

Official Explanation

Argument Construction

Which one of the five answer choices is most reasonable to infer from the information given by Mashika and Salim?

The information given allows us to make various deductive inferences. First, if each segment that significantly supports Ms. Puerta also significantly supports Mr. Quintana, then it follows, based on Mashika's statement, that no segment of the electorate that significantly supports Mr. Quintana also supports Mr. Ramirez. In other words, to support Ms. Puerta implies not supporting Mr. Ramirez; therefore, if the segments supporting Mr. Quintana include all the segments supporting Ms. Puerta, there can be no segments that support both Mr. Ramirez and Mr. Quintana.

However, Salim tells us that there is such a voter segment: at least one segment significantly supports both Mr. Quintana and Mr. Ramirez. From this, it follows that the hypothesis if those segments also provide support to Mr. Quintana must be untrue; in other words, there exists at least one segment of the electorate that significantly supports Ms. Puerta but not Mr. Quintana.

A. We are told that there is a segment that significantly supports both Mr. Quintana and Mr. Ramirez, but this provides no basis for concluding that there is also a segment that significantly supports neither of the two.

B. Correct. The previous explanation indicates that at least one segment supports Ms. Puerta but not Mr. Quintana.

C. If support for Ms. Puerta and support for Mr. Ramirez are mutually exclusive, then this must be false given that we know that at least one segment supports Mr. Ramirez.

D. The information provided indicates that this is false: there is at least one segment that significantly supports Ms. Puerta but not Mr. Quintana.

E. If support for Ms. Puerta and support for Mr. Ramirez are mutually exclusive, then this must be false given that we know that at least some segments support Ms. Puerta.

The correct answer is B.

A. At least one segment of the electorate provides significant support neither to Mr. Quintana nor to Mr. Ramirez.

Cannot be inferred.

B. At least one segment of the electorate provides significant support to Ms. Puerta but not to Mr. Quintana.

Salim says that at least one segment supports both Quintana and Ramirez but as per Mashika, if Puerta's supporters also support Quintana then Ramirez won't have any supporter's from Puerta's supporters.

This should mean that some of Puerta's supporters must support Ramirez and so these cannot support Quintana

B is correct

C. Each segment of the electorate provides significant support to Ms. Puerta.

Cannot be inferred.
D. Each segment of the electorate provides significant support to Mr. Quintana.

Cannot be inferred.

E. Each segment of the electorate provides significant support to Mr. Ramirez.

Cannot be inferred.

M : A segment can support P. That's fine. The fun begins in second statement. If segments that support P also support Q then no segment who supported Q supports R.

In our words: If P then Q then no R.

S: There is one segment that supports Q and R.

Pre-thinking: That means that one segment won't support P for sure.

Options:
A. At least one segment of the electorate provides significant support neither to Mr. Quintana nor to Mr. Ramirez. - We don't know. We just know the relationship established.
B. At least one segment of the electorate provides significant support to Ms. Puerta but not to Mr. Quintana. - That's true. Because we know some segments support P. But there has to be at least one segment that supports P but not Q for Q+R to hold true. Because if any segment supports P and Q then it cannot support R.
C. Each segment of the electorate provides significant support to Ms. Puerta. - If each supports P then Q + R will never be possible.
D. Each segment of the electorate provides significant support to Mr. Quintana. - We don't know.
E. Each segment of the electorate provides significant support to Mr. Ramirez. - We don't know.

B is the winner.!

Consider 10 segments: S1 S2 S3 S4 S5 S6 S7 S8 S9 S10

From Mashika's statement: Some segements provide support to Ms. P - Let those segments be S1 S2 S3 S4 S5 Thus P = S1 S2 S3 S4 S5
The second statement is really important to understand, If those segments. This means there are two types of segments in this case - some that support Mr Q. and some that do not support Mr. Q (they may support some X, but we do not know who). Thus let us consider that S3 S4 and S5 support Mr. Q and S1 and S2 do not support Mr. Q
Thus Q = S3 S4 S5
and these do not support Mr. R

From Salim's statement: At least one segment does support Mr. Q and Mr. R significantly.
Now S1 and S2 - do not support Mr. Q
S3 S4 and S5 - support Q but cannot support R
Thus there will be S6 S7 S8 - that support Mr. Q and support Mr. R
However, we are unaware of S9 and S10 - these can support Mr. Q and Mr. R or they may not support - This is not told by the argument.
Thus in total
Mr P = S1 S2 S3 S4 S5
Mr Q = S3 S4 S5 S6 S7 S8
Mr R = S6 S7 S8
S9 S10 = can support Mr Q or not support Mr Q - unknown


Option analysis:
Option A - False. Probable segments S9 and S10 - But as mentioned before - we cannot be sure. There is still a possibility that they can be supported by Mr Q.
Option B - True. Segments - S1 and S2
Option C, D and E - All can be proven to be false by the example stated in the "analysis".

Thank you.

GMATNinja,
VeritasKarishma
egmat

I do understand why (B) is the correct answer, but If there is at least one segment that support to Ms. P but not to Mr. Q, isn't true that there will be at least one segment that provides significant support neither to Mr Q nor to Mr R?

A. At least one segment of the electorate provides significant support neither to Mr. Quintana nor to Mr. Ramirez.
B. At least one segment of the electorate provides significant support to Ms. Puerta but not to Mr. Quintana.

Mashika's argument
IF: P -> P+Q
Then: No Q+R

However, “No Q+R” must always be true whether the IF happens or not. In other words, there must not be any segment that provides support to both Q and R in the first place. Otherwise the IF-THEN will not happen. Thus the IF is useless in this case, since THEN will always happen.

IF or XIF: P -> P+Q
Then: No Q+P

When Salim comes with the info that there is actually Q+P, we can interpret that “X THEN.” But does that mean “X IF” as the answer suggests? IMO, the “X THEN” completely destroys the argument instead of refuting it, thus leaving the “IF-THEN” unreasonable. Otherwise, you need to fix the paradox before justifying the answer.

Very simple explanation

As you can see in attached picture, B stands right in both cases. A may be correct in case 1 as shadowed area but fails in case 2.

VeritasKarishma
Plz help with this one:

SAy segments are S1,S2,23,S4,S5,S6,S7,S8,S9,S10
Now S1,S2,S3,S4 support Puerta

Quintana: say supported by S5,S6,S7,S8
If those segments also provide significant support to Mr. Quintana(what does this mean , if those - so S1,S2,S3,S4 all of these right?)

now Q has supprt of S1-S8
So R can have S9 and S10 only.
But Salim says :
at least one segment of the electorate does provide significant support to both Mr. Quintana and Mr. Ramirez.
say S9,S10 common btwn Q AND R
so now Q has S1-S10 everything

B)At least one segment of the electorate provides significant support to Ms. Puerta but not to Mr. Quintana.

How is this possible:
now P has S1-S4
and Q has S1-S10

Can u plz explain this in terms of given example.

I'll try to answer your question. I believe this may help others understand the dialogue and its implications as well.

Sure. Let's stay with these allocations.
Total segments: S1-S10
P: S1-S4
Q: S5-S8

You're right. "Those segments" refers to segments that support P.

Ok, wait a minute here. Let's understand this point clearly. We're presented with a conditional. If X happens, Y will happen. This on its own does not mean that X will happen.

If I see an ice-cream truck, I'll buy an ice-cream.
Does this statement mean that I will see an ice-cream truck for sure? No. If I see one, I'll buy an ice-cream. I might or might not see one.

If it rains later, I'll carry an umbrella. Does it mean that it WILL rain later? No. It might or might not.

We initially allocated S5-S8 as supporters to Q. This conditional WILL NOT change our understanding of who's supporting whom. As per our initial allocation, the 'if case' is not satisfied. S1-S4 DO NOT support Q (since only S5-S8 support Q).

Ok, let's understand this aspect as well now. What if the "if case" is not met?

What if I do not see an ice-cream vendor?
Does that mean I'll not buy an ice-cream for sure?
I might still stop at an ice-cream store and get a scoop.
Of course, I might not stop elsewhere and end up not buying an ice-cream.

What if it doesn't rain later?
Does that mean I'll not carry an umbrella for sure?
I might still carry an umbrella for shade from sunlight.
Of course, I might decide not to carry an umbrella too.

If the "if case" is not met, the "then case" may or may not hold. So, with the allocations for P and Q that we have made, the "if case" is not satisfied, and therefore there are no restrictions on who all can support R.


Hope things thus far are clear. To understand Salim's response better, I'll now CHANGE our initial allocations.



Fresh case:

P: S1, S2, S3, S4

If S1-S4 (segments that support P) also support Q - i.e., if at least all of S1-S4 support Q (Q might have other supporters too)
Q: S1, S2, S3, S4, ... (?)

Then, there is no overlap between Q and R supporters.
Say, Q: S1-S8
Then, R: None, S9 alone, S10 alone, OR S9 and S10


Right. So, there is an overlap between Q and R. i.e., the "then case" of Mashika's conditional is actually not true. What then?

If the "then case" does not hold, then the "if case" certainly must not have been true.

What if I DID NOT buy an ice-cream? Is it possible that I had still seen an ice-cream truck? It isn't. The initial conditional was: If I see an ice-cream truck, I will buy an ice-cream. Had I seen a ice-cream truck, I would have bought an ice-cream for sure. If I didn't buy an ice-cream, I for sure didn't see an ice-cream truck.

What if I DID NOT carry an umbrella? Is it possible that it did rain later? It isn't. The initial conditional was: If it rains later, I will carry an umbrella. Had it rained later, I would have carried an umbrella for sure. If I didn't carry an umbrella, it for sure didn't rain later.

If there is an overlap between Q and R supporters, that means that the "if case" must not have been true in the first place. So, all of S1-S4 (P's supporters) could not have supported Q. At least one of the four segments S1-S4 must not have supported Q.

In line with what we just figured out.



A case for you to think about:

What if:
P: S1-S4
Q: S2-S8

Do "those segments (P's supporters) also provide significant support to Mr. Quintana"?


Hope this helped. Of course, feel free to come back with questions in case anything is unclear.

Thankyou so much for the reply.
So those segments mean P: S1-S4
any of those segments and not all of those segments.right?
i.e why Q: S2-S8
and S1 has been excluded.
If it is all of those then S1 has to be in Q.m i right?

When you take an example, you need to ensure that all assertions hold true.

A1 - Some segments of the electorate provide significant support to Ms. Puerta.
A2 - If P's segments also provide significant support to Mr. Quintana, then no segment of the electorate that provides significant support to Mr. Quintana provides significant support to Mr. Ramirez.
A3 - At least one segment of the electorate does provide significant support to both Mr. Quintana and Mr. Ramirez.

All three need to hold.

As per your data:
P has S1-S4 (some segments provide support to P - A1)
Q has S5-S8
R has S9 and S10

A3 - We know that at least one segment supports both Q and R. So say S9 and S10 support both Q and R.

P has S1-S4
Q has S5-S10
R has S9 and S10

Now, there is a conditional statement:
A2 - If P's segments also provide significant support to Mr. Quintana, then no segment of the electorate that provides significant support to Mr. Quintana provides significant support to Mr. Ramirez.

- But we already know that there is at least one segment that provides support to both Q and R. This means, the condition is NOT satisfied. All P's segments do not provide support to Q. There is at least one segment that supports P but not Q.
That is how we arrive at (B)

My pleasure.

What "those segments" points to in the 'if condition' will not change based on how we allocate segments in our hypothetical example.

And, what segments support Q does not depend on the "if condition".

S1 doesn't have to be included or excluded.

The question I posed was:
IF, P: S1-S4
AND Q: S2-S8,
THEN, for this particular example, do "those segments" (P's supporters) also support Q?

And the answer is No. Since not all segments that support P also support Q.


1. My shirt has stains. Those stains were caused by paint.
2. My shirt has stains. Some of those stains were caused by paint.

Do both these mean the same thing? They don't. In the first example, all stains were caused by paint. In the second one, at least one stain was caused by paint.

Hello AndrewN - I think with this question I hit a roadblock. I got to the right answer by POE but I cannot seem to understand how it worked. I tried using formal logic from LSAT with negation but I cannot make sense of this question or how the correct answer leads to. I went through every single explanation twice, spent about 1.5 hour on this and now seeking some help if there's a way to decode this premises and how this answer choice is correct, maybe I am missing something, can you please help? Thanks.

Hello, IN2MBB2PE. Similar to the other recent CR question you asked me about, which was also from GMAT Advanced, this one has three variables to track: we can call them P, Q, and R. The passage and question stem, for reference:

You do not have to use formal logic symbols to keep track of the information. Mashika states that some segments... provide significant support to P. This is a statement of fact—we know that P has supporters. Then comes a conditional: if P and Q, then no segment... that provides significant support to Q also does so to R. Be careful here, or you can lose sight of P in the conditional.

Salim states that at least one segment... does provide significant support to Q and R. This is another statement of fact—we know that Q and R have mutual supporters.

Thus, if the two assertions are both accurate, we can infer just what answer choice (B) says, that some people—at least one segment—support P but not Q. Otherwise, what Salim asserts could not be accurate. If it helps, strike some of the overlapping language. These extra modifiers can hinder our understanding of the vital meaning of an answer choice.

This sounds a lot like what I just wrote above. Understand, I am not advocating striking out all modifiers when you assess an answer choice—doing so can get you into trouble pretty fast. But if the words all match up, and there is no distortion in how the information is presented, then you may find it useful to strip down the answer choice to its essentials to test for fidelity to the passage.

Thank you for thinking to ask.

- Andrew

This is a formal logic theorem that shows up often enough that it is ABSOLUTELY worth knowing COLD. Spend some time with it until you are fluent.
Let's use A = "I do too many GMAT problems" and B = "I get a headache"
A --> B: If I do too many GMAT problems, I get a headache.
Does "if I did NOT do too many GMAT problems" tell us anything about whether I got a headache? Nope, maybe I got hit in the head. So, "if I did not do too many GMAT problems" doesn't tell us anything. In formal logic terms, -A doesn't tell us anything.
Does "if I have a headache" tell us anything about whether I did too many GMAT problems? Nope, maybe I got hit in the head. So, "if I have a headache" doesn't tell us anything. In formal logic terms, B doesn't tell us anything.
Does "if I DON'T have a headache" tell us anything about whether I did too many GMAT problems? Oh, now that does tell us something. If I don't have a headache, I must not have done too many GMAT problems. In formal logic terms, -B --> -A
So, the only thing we know from A --> B is that -B --> -A.
That is, if we move whatever is on the right side to the left side and negate it, we can move whatever is on the left side to the right side and negate it, too.

Okay, on to the question.

Mashika: P+Q --> -R
Salim: Q+R

From the above in red, we can get from Mashika's comment that R --> not (P AND Q)......maybe P or maybe Q, but we can't have both. Make sure you think about and understand how to handle AND and OR on something like this.
Salim tells us that R AND Q.
If R, we can't have both P AND Q. We know we have R, so we can't have P and Q. We have Q. That means we can't have P.

Answer choice C is perfect.

My approach using triple venn diagram and supporting areas of overlap and non-overlap:

I like to think of it this way to avoid confusion.

M: Some segments support P
If all of these segments(all P segments) support Q -> No one who support Q support will support R

S: At least 1 segment support both Q and R

Gist:
P,Q,R
Possible combos since order doesn’t matter. Only inclusion or exclusion matters.

1: P Q R
2: Q R
3: P Q
4: P R
5: P
6: Q
7: R
8: -

Stuff that must be true:
a. Some P segments exist
b. At least 1 Q and R supporter
c. All P doesn’t support Q since 2 is true.

A. At least one segment of the electorate provides significant support neither to Mr. Quintana nor to Mr. Ramirez.
Wrong: 5 and 8. But, they are not must exist for above statements. Even after their removal, all 3 statements works fine.
B. At least one segment of the electorate provides significant support to Ms. Puerta but not to Mr. Quintana.
True: there are 4, 5 and 8 and 4 or 5 is a must.
C. Each segment of the electorate provides significant support to Ms. Puerta.
Wrong: 2 , 6, 7 and 8 can exist.
D. Each segment of the electorate provides significant support to Mr. Quintana.
Wrong: similar to C
E. Each segment of the electorate provides significant support to Mr. Ramirez.
Wrong: similar to C­