Let S be a set of 6 integers taken from {1, 2, ..., 12} with the prope

Question

Let S be a set of 6 integers taken from {1, 2, ..., 12} with the property that if a and b are elements of S with a < b, then b is not a multiple of a. What is the least possible value of an element in S?

A. 2
B. 3
C. 4
D. 5
E. 7

A. 2
B. 3
C. 4
D. 5
E. 7

BrentGMATPrepNow · Answer

Let's first determine the SMALLEST possible value in set S

1 cannot be the SMALLEST value, since every remaining value is a multiple of 1

Can 2 be the SMALLEST value?
The remaining five values cannot be even (otherwise, they will be a multiple of 2) 
We get: {2, 3, 5, 7, 9, 11}
No good. 
9 is a multiple of 3. 
So, 2 cannot be the SMALLEST value,

Can 3 be the SMALLEST value?
Let's starting listing the other values: {3, 4, 5, 7, 11, ?}
We cannot add a sixth value without breaking the rule of numbers not being multiples of other numbers.

Can 4 be the SMALLEST value? YES!!
We get: {4, 5, 6, 7, 9, 11}

Answer: C

Cheers, 
Brent

Archit3110 · Answer

we can solve this question using answer info
option a; 2; we can have set ; (2,3,5,7,9,11) ; but 3 is factor of 9 or say multiple of 9 insuffiient
option b ; 3 ; (3,4,5,7,11,) ; 6th value cannot be determined as range is from 1-12
option c; 4 ; (4,5,6,7,9,11);sufficient
IMO C ; 4

ScottTargetTestPrep · Answer

Let’s start with 2 as the smallest number, as 1 is not among the answer choices. We can have 2, 3, 5, 7, 11 in our set. However, since any other number we will add will either be a multiple of 2 or a multiple of 3, this set of numbers does not work. Also, there are no numbers in the set which will enable us to add more than one number if we don’t include (for instance, if we don’t add 3, we will be able to add 9 but we still have five numbers. If we don’t include 5, we will be able to add 10 but we still have five numbers).

Now, let’s try 3 as the smallest number. We can have 3, 4, 5, 7, 11. However, again any other number we add will be a multiple of a number that is already in the set (6 is a multiple of 3, 8 is a multiple of 4, 10 is a multiple of 5 etc.) Again there are no numbers which would make it possible to add more than one number if not included, similar to the above case.

Let’s try 4 as the smallest number. We can have 4, 5, 6, 7, 9, 11. We see that we have followed the rules for the set, so 4 is the smallest possible number.

Answer: C

bumpbot · Answer

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Let S be a set of 6 integers taken from {1, 2, ..., 12} with the prope

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Let S be a set of 6 integers taken from {1, 2, ..., 12} with the prope

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