Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y

Question

Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X?

(A) 14
(B) 16
(C) 17
(D) 20
(E) 26

manpreetsingh86 · Accepted Answer

y = product of all elements in set X. now, y will be even if 2 is part of this set (k=2), else y will be odd.

since we have, 11y as an even integer. therefore y must be even. (because 11 is odd, therefore the only way in which 11y can be even is when y is even.)

thus elements in the set X are {2,3,11,7,17,19} and thus its range is 19-2=17

dmmk · Answer

Since 11Y = Even therefore Y has to be  EVEN  since 11 is a odd integer (Even * Odd = Even)

Similarly, Y is the product of all integers in set X But all integers in Set X are odd except the unknown K and since X contains only prime numbers, K has to equal to 2... ( 2 is the only even prime number and the product of all prime numbers in set X has to be Even, Even * Odd = Even)

Since you know value of K you can calculate the range = Largest integer in the set minus Smallest integer in the set = 19-2 =   17

Answer is C

PareshGmat · Answer

Just observe the numbers given in the set

{3, 11, 7, K, 17, 19}

All numbers are odd & prime, so there product is also odd

Given that 11y is even number (Again 11 is odd; so y has to be even)

The only prime number which is even = 2

So, for k = 2, range = 19-2 = 17

Answer = C

PareshGmat · Answer

One more method:

Just observe the OA

(A) 14 
(B) 16 
   (C) 17    
(D) 20 
(E) 26

Once we are convinced that k = 2, then

Odd - Even = Odd

Only option C fits in;   all other options are Even suggesting that "k" would be ODD which is not the case

Answer = C

AkshdeepS · Answer

Bunuel,

How would we know whether 11Y is a 3 digit integer with unit digit as Y or it is a product of 11 * Y?

Bunuel · Answer

If it were a three-digit number it would have been explicitly mentioned. 11y is 11*y, recall that only * sign could be omitted.

ManviGupta · Answer

The product of 11Y is an even number, therefore Y would be even and if you look at the prime numbers in set X all are odd, therefore K would be even to get 11Y even. So we need an even number in the set, which would be K, lowest number.
As per equation: Range = Highest –Lowest 
(A) 14 (19-14=5)
(B) 16 (19-16=3)
(C) 17 (19-17=2)
(D) 20 (not possible, greater than 19)
(E) 26 (not possible, greater than 19))

DivyaYerranagula · Answer

Why should we consider k=2 only , why can’t we take k=4,6,8...
Plz help.

Posted from my mobile device

masoomjnegi · Answer

11Y will be even if Y is even.
Y = product of all elements in the set. 
There is no even no in the set X. So, ‘k’ should be even to make y even.
There is only one even prime no i.e. 2. So, k = 2
The set X becomes {2, 3, 7, 11, 17, 19}.
Range of the set = highest element – lowest element = 19 – 2 = 17

SWAPNILP · Answer

Hi Divya

We cannot take any other even nos because they are not primes and it is clearly mentioned that set consists of prime nos and integer 2 is the only even prime no.

Hope it helps

ScottTargetTestPrep · Answer

Since 11Y is even, Y is even and hence K must be even also. Since 2 is the only even prime number, K is 2. Thus, the range of set X is 19 - 2 = 17.

Answer: C

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Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y

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Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y

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