Data Sufficiency

Hi @Taran:

Lets assume that a small subset of no's q is in Q. now for every no, a, in this subset we know that a+11, a+22, a+33.... are in the set. Now we know foresure that 11 is in the set from stem so irrespective of other no's at least 11, 22, 33, 44......are in this set. so you can;t restrict it to only "100" multiples of 11, rather infinite multiples of 11 are present.

HTH,
Kats

Taran wrote:Hi Guys,

What is the source of this question? Anyhow, i found the question very vaguely drafted.

1. It asks whether the Set Q contains 'every' positive multiple of 11. What if the set is {11, 22, 33, 45, 21, so on......}. In this case, we can assume q to be any integer. Considering this, we will always have positive multiples of 11. My doubt, here is that what if q is 2 and all q+11's are in the set, but only 100 multiples of 11 are there. I hope my question is clear to all.

1 alone is sufficient

I have a slightly different take on this question.

Q is a set of integers and 11 is in Q. Let q denote any element in the Q set. Is every positive multiple of 11 in Q?

1. q + 11 is in Q
2. q - 11 is in Q

Stated: 11 belongs to set Q; 'q' is any element in set Q.

Statement#1: Let q=11. Thus q+11=22 also belongs to set Q.
Let q=22. Thus q+11=33 also belongs to set Q.
Similarly, 44, 55... all belong to set Q

SUFFICIENT.


Statement#2: q - 11 is in Q. But we know that 11 too is in set Q.
This allows us to create the equation q - 11 = 11, ie, q=22 belongs to set Q.
In the same way, q - 11 = 22, ie, q=33 belongs to set Q.
Similarly, 44, 55... all belong to set Q

SUFFICIENT.

This makes either one of these statements sufficient to solve the problem.
Thoughts, anyone?

milanproda wrote:Q is a set of integers and 11 is in Q. Let q (small q) denote any element in the Q set. Is every positive multiple of 11 in Q?

1 q+11 is in Q

2 q-11 is in Q

stmt 1- if q is a positive multiple of 11, then q +11 must be multiple of 11

stmt 2- if q=121, then q-11=110 (OK)
if q =11 then q-11 equals 0 .since 0 is neither positive ,nor negative, stmt 2 is insuf

OA is A

This is what is defined as a recursive loop!

q+11 is available in Q and 11 is available hence all multiples of 11 are available i the set.
Same cannot be said of the other set.
(A) is answer

For statement 1 - Why cant we denote q = -11. In this case +11 would still be in set Q but not every q would be a positive multiple of 11. Please advise. Thanks!

Anurag@Gurome wrote:

milanproda wrote:Q is a set of integers and 11 is in Q. Let q (small q) denote any element in the Q set. Is every positive multiple of 11 in Q?

1 q+11 is in Q

2 q-11 is in Q

Given: Q is a set of integers and 11 is in Q.
Now q denote any element in the Q set. Note that this means any element of set Q can be taken as q.

Statement 1: (q + 11) is in Q
We know that 11 is in set Q. Therefore we can say q = 11. This implies (q + 11) = 22 is in Q. Now we can say q = 22, thus (q + 11) = 33 is in Q. Thus 44, 55, 66 etc all are in Q. Which means all positive multiples of 11 are in Q.

Sufficient

Statement 2: (q - 11) is in Q
We know that 11 is in set Q. Therefore we can say q = 11. This implies (q - 11) = 0 is in Q. Now we can say q = 0, thus (q - 11) = -11 is in Q. Thus -22, -33, -44 etc all are in Q. Which means all non-positive multiples of 11 are in Q. But nothing can be said about positive multiples of 11.

Not sufficient

The correct answer is A.

milanproda wrote:Q is a set of integers and 11 is in Q. Let q (small q) denote any element in the Q set. Is every positive multiple of 11 in Q?

1 q+11 is in Q

2 q-11 is in Q

Answer: 1- Statement 1 is sufficient, but statment 2 is not sufficient

Thanks! If anyone has time, please explain the answer thoroughly becuase I am having trouble understanding it.

My understanding

q+11 = 22
22+11 = 33
33+ 11 = 44 ...

33-22= 11
22-11=11

but 11-11 =0
which is not a multiple

A in answer.

well i m pretty late to reply here.. but i took the question differently:
well if q+11 is in Q and knowing that 11 is in there then can we not say there MUST BE a value of q which satisfies this relationship with 11 as:
q+11=11
q=0
which means 0 is in Q
and the question is every positive multiple of 11 in Q .. hence 0 is not a positive multiple of Q the answer must be No?

OR do we say that question says that every positive multiple of 11 has to be there in Q irrespective of few other numbers which are not positive multiple of 11 so even if 0 is there it doesnt matter as far as all positive multiples of 11 are there..
something like we do in CR it is a must that X contains Y but not a must that X contains ONLY Y..

Is any approach right??

OA is A

Q is a set of integers and 11 is in Q. Let q denote any element in the Q set. Is every positive multiple of 11 in Q?

1. q + 11 is in Q
2. q - 11 is in Q

I didn't get this question 100%.
Multiples of 11 are 11, 22, and so on
if q=11, then 11+11 =22, then answer should be A.

This question is quite confusing.