A boarding school accommodating 400 students has provided a locker to

Question

A boarding school accommodating 400 students has provided a locker to each student. On Christmas eve, Santa places a pen in every other locker, a box of chocolate in every third locker, and a bottle of wine in every fifth locker starting with the second locker for a pen, the third one for a box of chocolate and the fifth one for a bottle of wine. How many students have got none of the three gifts?

A. 11
B. 12
C. 13
D. 14
E. 15

A. 11
B. 12
C. 13
D. 14
E. 15

Fdambro294 · Answer

is there something wrong with either the question or the answer choices?

out of the 1st 40 lockers, the following lockers will not receive a gift:

1 , 7 , 11 , 17 , 23 , 29 , 31 , 37

that is 8 lockers already in the 1st 40 lockers with 360 more lockers to go. There are many other Numbers that are not multiples of 2 , 3 , nor 5. There exists 46 Prime Numbers alone from 1 through 200 (add a 47th locker for the 1st)

Unless I am misunderstanding the question?

rahulbhusan · Answer

As per the given information in the question stem, we have following details:-

Pen is placed in Locker numbers....................2, 4, 6, 8.....400
chocolate is placed in Locker number.............3, 6, 8.........399
A bottle of wine is placed in Locker number....5, 10,15,......400

Locker number 6 will have Pen and a Chocolate (because 6 is a multiple of 2 and 3), similarly Locker number 10 will have a pen and a bottle of wine (because 10 is a multiple of 2 and 5)

so, to find the locker that has all three gifts, we need to find the LCM of 2,3, and 5 = 30
so, locker numbers will be 30, 60, 90...390
This now becomes a simple AP series, and we just need to find the number of terms in this AP series.
Total Lockers that contain all three gifts (No. of terms in the above AP Series)= 
(Last Term- First Term)/ Common Difference + 1
=> (390-30)/ 30 + 1
=> 13
The above question has a typo, as if we want to find NONE of the students who have received all 3 items, 
then is correct answer will be 400-13= 387.

So, based on the options, I believe we are asked to find "students who have received all 3 items"
So, Our answer is   option C

Fdambro294 · Answer

but doesn't the question ask: "how many students have got NONE of the 3 gifts?"

I think that is the correct answer to the correct intended question. I believe it is a question from Wizako that was testing LCM concepts.

rahulbhusan · Answer

I believe that must be a typo, else the options won't make sense.

If we want to find the number of students who have got NONE of the 3 gifts, the correct answer will be 400-13= 387
I hope that is clear?

Fdambro294 · Answer

Yup, we’re on the same page

Posted from my mobile device

kush09 · Answer

Looks like question is not correct, because what question is asking is all numbers between 1 to 400 whcih are not divisible by 2, 3 and 5.

Below are the list of prime number, which it self is far greater than an possible answer choices.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397.

And apart from this we have numbers like 77 and 91 which are not divisible by 2, 3, and 5.

Please correct the question. Thanks.

A boarding school accommodating 400 students has provided a locker to

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