Data Sufficiency: Yes/No Questions

fluke - i have spent some time applying these questions to problems while doing DS problems, and I have spent time reflecting on my mistakes in error logs.

It still seems I am getting mainly D.S. (Yes/No) questiosn wrong more than any other type. [maybe DS - Y/N are more prevalent than DS value?]
Out of all of your questions I notice that I do not always test ALL of the cases...

also, I have noticed I have a difficulty on DS-Y/N questions that deal with divisibility, although I understand what divisibilty means.

Any ideas of how to tackle these problems I have identified?

Thanks a lot
-Tom

Please go through following topics in the link provided:

math-number-theory-88376.html
Factors, Greatest Common Factor (Divisior) - GCF (GCD), Lowest Common Multiple - LCM, Divisibility Rules, Consecutive Integers.

Also,
compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html

If you like you can present us with a real DS question(which you did wrong) and your train of thoughts, the analysis and approach when you solved it. Note: please don't see the explanation of the answer till we discuss it. Just remember to jot down your approach as soon as you see a wrong answer.

Let's do it.

perfect. ill look at those and I am taking another practice CAT tmw. so ill write down and post the approac before looking at the explanation and making my error log

Question:
If p < q and p < r, is pqr < p?

(1) pq < 0

(2) pr < 0

analyze question:
is pqr-p < 0?
p(qr-1) < 0?
find the sign of p and (qr-1). if they are opposite, it is (-), or less than 0

(1) pq < 0, so they must be opposite signs
since p < q, p must be negative and q is positive.
no information about r, so we don't know the expression (qr-1), thus Insufficient

(2) pr < 0, so they must be opposite signs
since p < r, p must be negative and q is positive.
no information about q, so we don't know the expression (qr-1), thus Insufficient

(T) Looking back (I'm trying to remember exactly what I did with the statements together. I think I just tried to think about what it would be, but I don't remember plugging in any concrete examples...I know my final answer was C, so I think I just tried to rationalize it and after thinking about it for a few moments figured it should be sufficient together...I'm guessing I let the stress of the test get to me and didn't go through it logicially

[sitting here analyzing it with more time, I see:
basically I need pq-1>0 or pq > 1.
p and q are both positive, but they could be less than 1 or greater than one creating an answer of YES or NO, thus insufficient
answer is E]

Another question I answered incorrectly:

If x is a positive integer, is x! + (x + 1) a prime number?

(1) x < 10

(2) x is even


the only way I was able to simply this question stem is "can X! + (x+1) be divided by any other number?" and X! + (x+1) = x*(X-1)*(x-2) etc + (x+1)

I started with (2). if x is even, (x+1) = Odd, and x! must be even, so odd+even = odd, so there is a better chance it is prime (at least its not even)

(1) I just tested some cases that are less than <10, but not all of them because I didnt want to waste time.
x=2 --> 2+3 = prime,
x=3 --> 6+4 = not prime
Thus insufficient

(T). I think I tested a couple cases of evens less than 10, working my way up, but not all of them (i stopped at x=6)
x=2 --> 2+3 = prime,
x=4 --> 4*3*2 + 5 = 24+5 = 29
x=6 --> 6*5*4*3*2 + 7 = 720 + 7 = 727
maybe i should test all the divisibility rules now. I do not know all of them by heart yet. I MAY have tested 3 (7+2+7 = 16, thus not divisible by 3)
at this point I think I just concluded that 727 was prime, and thus all of the even integers less that 10 put into this formula create a prime number, thus Sufficient
--> looking back, my answer was B, I guess because I decided from this small pattern that all even integers in this formula create prime numbers

...I probably sound pretty ridiculous with my pathetic reasoning in these posts, although I consistently score 44-49 on Quant, but I want to consistently score 45-50. [I guess this answers your above post --> the questions I am missing do tend to be difficult, upper level questions.

I will post another example or two tomorrow...but do these explanations suffice?

This is a difficult question: 650-700 level.

Your approach is perfect; I think the only reason that you didn't answer correctly was the panicky state. Also, trust what you think while solving a question. You can question yourself whether what you are thinking is fully correct; if you doubt yourself too much, it's going to make your jittery and can potentially make you choose a wrong answer. So, just trust your approach.

Moreover, I believe you are in-line with approaching DS questions. These few errors can be handled with enough practice. You would know the patterns to solve a specific question as soon as you see it if you practiced enough questions before.

This question is unique in its own sense.

I see that there are certain typos in your explanation. Where p should be -ve, you have written p is +ve. Guess those are just typos.

Here's how I would approach this, and I must tell you that my approach is exactly 99% same as yours;

If p < q and p < r, is pqr < p?

(1) pq < 0

(2) pr < 0

Rephrase:
pqr-p<0
p(qr-1)<0
p & (qr-1) should have opposite signs.

(1) pq<0
p AND q have opposite signs.
p<q
Thus,
p=-ve
q=+ve

Now, at this point, rather than saying that r is not known and it's insufficient. I would still validate my expression quickly. Perhaps there is no necessity, but it makes me more aware of the third variable r existence.

rephrased expression:
(-ve)*[r*(+ve)-1]

p=-1
q=1

PIN;
r=1000000000000000000000(some big number)
[r*(+ve)-1]-> +ve
+ve*-ve=-ve

r=0.000000000000000000000000000001
-ve*-ve=+ve

Note: Please do these PIN in your head. You may think that combining PIN with algebra may be unnecessary and time consuming but in my opinion it definitely increases one's chances to answer correctly.

(2)
pr < 0
And we know that p<r
p=-ve
r=+ve

p=-1
r=1
p(qr-1)

q=10
-1*(1*10-1)=-ve

q=-0.5
-1*(-)=-ve
Not Sufficient.

We know;
p=-ve
q=+ve
r=+ve

p(qr-1)
q and r are both positives, but it may be less than 1 or more than 1.
q=0.00001; r=0.000001; qr<1
q=10;r=10; qr>1

Thus,
p(qr-1) may be >0 or <0.
Not Sufficient.

If you take 1:50 minutes to solve this question, it doesn't matter. Just solve it correctly.
Correctness > Speed

Because, you will get 7-8 questions where you will save the time. So, just don't panic.
Time spend in guessing on a difficult questions that you know you can't solve. max 30 secs.

Time spend in guessing a relatively difficult question that you know you can solve given 3 minutes. go ahead and solve it.
******************************************************************************************

Another tip for PIN;

Plugging in number is great to prove an expression insufficient. 100% But, it is not so good to prove sufficiency.
Algebra; if executed completely will give a definite answer, yet it is advisable to testify your results with PIN.
******************************************************************************************

I categorize this question as another difficult question. 650-700 level.

Reasons:
1. This question seems difficult.
2. The number plugging may result in incorrect answer, at the same time plugging would be better approach to solve this.
3. Difficult to rephrase or to shorten.

For this questions, I won't solve each statement independently. I'd rather take the reverse approach. Call it hunch if you may.

So, I assume St1 and St2 to be true and try to solve it.

Integer less than 10 and even.
2,4,6,8
Write them down in values;
2!+3
4!+5
6!+7
8!+9

Here, my knowledge of factorization tells me that 8!+9 will not be prime and rest everything will be;
This will be true for all x+1: that are prime

How so; let's see
2!+3=2*1+3 --- Here from the two terms I can't take anything common
4!+5=4*3*2+5 ---Here also from the two terms I can't take anything common
6!+7=6*5*4*3*2+7---Here also from the two terms I can't take anything common
8!+9----- 8*7*6*5*4*3*2+3*3=8*7*(3*2)*5*4*3*2+3*3=3*3(8*7*2*5*4*2+1) -- Here since I took 9 common from both terms, I am certain that the entire expression is divisible by 9 and thus NOT prime.

Now, here I used both the statements true and yet couldn't prove its sufficiency. Thus, the statements must together be insufficient.
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Now, why couldn't you do it. Just because you didn't know the pattern to solve such type of questions. Now you know it and henceforth can apply this factoring common value from both terms. The more problems you do in factorials, the more acquainted you will become with the patterns and start solving such questions faster and without error.

Thus, I would say two things for this.
Practice and doubt a little your plugging number method when you are using it as basis to declare a statement sufficient.
PIN- Good to make expressions/statements insufficient.
PIN-NOT so good to make expressions sufficient.
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I recommend this. Chances of finding a question that you did incorrectly are really good. Thus, search for a particular question that you missed and see whether you get an appropriate/satisfactory answer in the discussion. If not, just reply in the same thread so that others may get a chance to look at it and suggest various strategies to solve that.
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All the best!!!

awesome replies...a couple of questions along these lines, on the few things I don't understand.

were you referring to my analysis of the statements together (i see I should have said [qr>1}, whereas I was saying pq>1 [I said p instead of r].
looking at the analysis of statements seperately, I think everything is referred to correctly tho.

i understand your approaches and analysis well... for the second problem, is there a definite reason you can explain so I can put it into practice regarding why you went straight to analyzing (1) + (2) together? is it because you could already tell they must be sufficient together or not at all? Or maybe because each statements by themself would take a long time.
(but if they worked together you would then have to look at them seperately, right?)


So you think my process is correct, and now I just have to work on mastering and becoming familiar with the topics applied difficult questions?



Lastly, can you elaborate on this:
I have heard it before, but it never seems to stick. if you elaborate (also including why it is true) i think it will help it stick in my head and thus help me apply the idea.

Thanks so much! i'm very grateful!

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