Data Sufficiency Questions
SBs for those that answer both questions correctly
- Set S consists of 20 different positive integers. How many of the integers in S are odd?
(1) 10 of the integers in S are even (2) 10 of the integers in S are multiples of 4
A Statement 1 alone is sufficient but statement 2 alone is not sufficient B Statement 2 alone is sufficient but statement 1 alone is not sufficient C Both statements 1 and 2 together are sufficient together but neither statement is sufficient alone. D Each statement alone is sufficient E Statements 1 and 2 together are not sufficient
- Does x=5? (1) x^2 = 25 (2) x =/= |x|
A Statement 1 alone is sufficient but statement 2 alone is not sufficient B Statement 2 alone is sufficient but statement 1 alone is not sufficient C Both statements 1 and 2 together are sufficient together but neither statement is sufficient alone. D Each statement alone is sufficient E Statements 1 and 2 together are not sufficient
ofcourse this is my opinion, but for Q1, statement 1 gives you enough info as all positive integers are by definition odd or even. since it doesn't state at least, then it's safe to say that there is 10 odd integers. For statement 2, integers can still be even without being multiples of 4. Take 10 for example. Thus, 2 tells us nothing. So I would say A.
For 2, statement 1 yields +/- 5, so there is not enough info. However, statement 2 tell us exactly that X does not equal +5. (this is assuming that =/= means not equal to. So C is your answer.
Expl.: (1) is sufficient. If 20 different POSITIVE integers are included in the set, 0 can't be an element. If 10 elements are even, theother elements must be odd. (2) is not sufficient because not it only gives you information about multiples of 4. But multiples of 2 are also even.
(1) is not sufficient because it gives you x = +/- 5 as a solution. (2) is not sufficient because if verified independently of (1), it could be any number.
Combined, (2) will tell you that the value from (1) can't be -5 because the absolute value of -5 is NOT -5. Therefore, the solution will be 5.
For Q1: Statement A is sufficient 1. A
For Q2
Since x^2=25 that means x= 5 or x=-5, you need to know if x=|x|, if so X=/= 5 therefore x=-5
2. C
A, C
Agreed for C on number 2.
However, for number 1, I think the answer is actually E.
"10 of the integers in S are even" is not the same as "exactly 10 of the integers in S are even".
"10 of the integers in S are even" is a description of only 10 numbers within S, and you have no idea what the other 10 are.
Everyone who is saying C for #2 is wrong. The second statement tells you the number must be negative, and therefore cannot be 5. The answer is B
Boothorbust,
The answer is not B. Basically what you are saying is this:
Question: Does x=5?
Your answer: Well if x=/=|x| then I have enough information to say whether or not X=5. Without A, B doesn't tell you much.
You do not need a discrete value for x, you just need to know whether 5 is a possible value for x. Statement 2 is enough to know that x cannot be 5.
Yes, I just tried to edit my comment, I see what you are saying, I was wrong. I'll give the excuse that I took the GMAT too long ago.
Are you guys sure 1 is E?
If statement 1 is saying that exactly 10 of 20 integers are even then it would be A.
That's how I would read it normally, but given these were supposed to be tricky I thought there was a catch and went with E.
1)A 2)B-----b alone proves x cant be 5 because x is neg
Yeah, I am going to guess E here for #1. I still think the question is poorly written- they don't give you any sense of what they're claiming they observed and what they didn't, but part of doing well on a standardized test is learning the exam's semantics.
The nice thing about a standardized exam is that these questions are carefully vetted to look read and mean like all of the other questions. So this ultimately comes down the College Board's semantics for how they report observations. Statement one either means "We observed 10 elements and they were all even", or it means "We observed all 20 elements and ten were even."
This is an important thing to learn before going into the exam. Thankfully I took my GRE's two years ago; they're largely written for obsessive STEM major types, so I don't think I remember any ambiguous questions like these.
IIRC when a gmat question says "10 are even" it means 10, not 9, or 11, or 10-20, but 10 are even.
Of course it means 10, not 9, are even. But it does not necessarily mean that "ten are even and we checked the other ten to make sure they're not."
This is just one of those places where getting lots of practice in for the GMATs and LEARNING the College Board's semantics on questions like these boosts your score by 20 points.
IMHO, better for OP to get this question wrong on his practice exam so he will remember it when he's taking the real thing.
I meant that the gmat question would say " at least 10" if there was even a possibility of more than 10 in the set being even.
pretty sure, but i will put in a disclaimer that i took the gmat almost a year ago and havent looked at any questions since :)
I call shenanigans if "10 of the integers in S are even" means that there are "exactly 10 even integers in S", and not "there are at least 10 even integers in S". That kind of molestation of the English language is acceptable in everyday speech, but certainly not on a standardized exam.
if "10 of the integers are even" does not mean "exactly 10" that is bullshit semantics just meant to confuse, and is a very poorly worded question.
E, C
1 could be A depending on how you read the statements.
The correct answer for 1 is A, according to the GMAT creators. The 2nd is obviously B, as has been explained above.
Yes, I know that from a math point of view, A is wrong for 1, but the GMAT writers seem to think this is fine. Pretty absurd if you ask me.
I really don't see anything absurd about it. The gmat is written in precise english so every answer is airtight, so 10 means 10, not 10-20.
a,b these are very straight forward and quite easy for data sufficiency, I assume the answers given by the answer book you are using differ from these?
But if I did, I would pick E.
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