If S is a set of integers and 5 is in S, is every multiple

Question

If S is a set of integers and 5 is in S, is every multiple of 5 in S?

(1) If x is in S, then x+5 is in S
(2) If x is in S, then x-5 is in S

agdimple333 · Answer

St - 1 ==> if X is in S, then X + 5 is in S, meaning X is in S then X + 5 is in S, if X+5 is in S then (X+5)+5 is in S and so on.. So if 5 is in S then 10 is in S, if 10 is in S, then 15 is in S.. and so on.
But see that questions ask you every multiple of 5 means even -ve.
So st 1 is not sufficient.

St - 2==> Same story as above... but other way. .. 0, -5, -10... are in S.

If you combine I and II than ....-10, -5, 0, 5, 10,... are in S i.e. every multiple of 5 is in S.

So C.

I came across this yesterday in knewton (i think) and found it little weird.

amit2k9 · Answer

a 0 is a multiple of 5 too. If first element is 5 means 5,10,15. Hence not sufficient.

b takes into account negative elements. Not sufficient.

a+b considers -5k<= multiple <=5k

hence C.

hussi9 · Answer

S=

Statment 1: 
5+5,
=>5+5+5 and so on for all =ve multiples of 5
S=  Not all multiples of 5 but have no clue of other components of S so insuff

stament 2:
5-5
S=  Not all multiples of 5 but have no clue of other components of S so insuff

Combining both S=

==> AND is C

Bunuel · Answer

If S is a set of integers and 5 is in S, is every multiple of 5 in S?

(1) If x is in S, then x+5 is in S. Since 5 is in the set, then 5+5=10, 10+5=15, 15+5=20, ... are also in the set. So, every multiple of 5 more than or equal to 5 are in the set. Though we cannot be sure about the multiples of 5 less than 5 (0, -5, ...). Not sufficient.

(2) If x is in S, then x-5 is in S. The same here: 5, 0, -5, -10, are also in the set. We don't know whether the multiples of 5 which are greater thatn 5 are also in the set. Not sufficient.

(1)+(2) All multiples of 5 are in the set. Sufficient.

Answer: C.

Similar questions to practice:
if-p-is-a-set-of-integers-and-3-is-in-p-is-every-positive-96630.html
k-is-a-set-of-integers-such-that-if-the-integer-r-is-in-k-103005.html
k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.html
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-x-136580.html
a-set-of-numbers-has-the-property-that-for-any-number-t-in-15554.html
a-set-of-numbers-has-the-property-that-for-any-number-t-in-t-98829.html

Hope it helps.

aankittcoolest · Answer

Hi ..one question..
Why can't we assume x to be any other integer such as 1,2,3,4,6...
In that case both the condtions will not suffice even after combination..
help plz..
Thanks

Bunuel · Answer

Please check the links provided in the post above. Your doubt is answered in that threads many times.

Consider (1): we are told that if some integer (x) is in the set then that integer plus 5 is also in S. This is a property of set S.

We know that 5 is in S, which means that integers 10, 15, 20, ... are also in S. But we cannot assume that there are any other integers in the set apart from these.

kusena · Answer

Set with all multiples of 5 shld contain {....-15,-10,-5,0,5,10,15....}

From Stmt 1) 5,10,15,.... will be present in Set S, 1 Alone not sufficient
From Stmt 2) 0,-5,-10,-15....will be present in Set S, 2 Alone not sufficient
Both together can ans the question,,Hence C

Hope its clear

thapliya · Answer

So isn't it that x can take any value, 
From the first statement the constraint is 5 should be in Set and if x is in the set then x+5 should be in the set:
So x = 0 implies that 0,5,10 ... are in the set
x= -5 implies that -5, 0, 5, 10 ... are in the set
x = -10 implies that -10, -5, 0, 5 ... are in the set
x = -100 implies that -100, -95, -90, -85 ... are in the set
and I think the same logic can be extended till -infinity ... So statement 1 is sufficient.

Same logic goes for statement 2 as well...

IanStewart · Answer

This is not a good practice question. The GMAT doesn't test 'negative multiples' of integers, so you'd never see something like this on the real test. GMAT divisibility questions are almost always explicitly restricted to positive integers, and if they're not, you'll get the same answer whether you think about zero and negatives or don't.

A lot of prep companies design questions like this, trying to be 'tricky', but practice questions that sensitize test takers to 'traps' the GMAT would never use are doing test takers a disservice. Any time a test taker spends, during a test, thinking about the 'trap' this question illustrates is time wasted.

bumpbot · Answer

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If S is a set of integers and 5 is in S, is every multiple

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If S is a set of integers and 5 is in S, is every multiple

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