A department of motor vehicles asks visitors to draw numbered tickets

Question

A department of motor vehicles asks visitors to draw numbered tickets from a dispenser so that they can be served in order by number. Six friends have graduated from truck-driving school and go to the department to get commercial driving licenses. They draw tickets and find that their numbers are a set of evenly spaced integers with a range of 10. Which of the following could NOT be the sum of their numbers?

A) 1,254
B) 1,428
C) 3,972
D) 4,316
E) 8,010

A) 1,254
B) 1,428
C) 3,972
D) 4,316
E) 8,010

D3N0 · Accepted Answer

Ans: D

Given 6 numbers that too evenly spaced with Range 10 so 
lets say least is x and bcz range is 10 so largest is x+10. This way we know these number will be
x, x+2, x+4, x+6, x+8 and x+10
Sum of all = 6x+30 or 6(x+5)
; the sum of these 6 number is multiple of 6. so from the given sum any sum which is not divisible by 6, can not be the sum of the those six numbers.

Ans: D

zishu912 · Answer

Given the range is 10

so let's assume that smallest number is x , therefore the greatest number will be x+10

also the number are evenly spaced and we need four numbers in between x and x+10, therefore x ,x+2,x+4,x+6,x+8,x+10

x+x+2+x+4+x+6+x+8+x+10 = 6x + 30 = sum of the all six numbers

Now working with each of the given option, we will find each of the number will satisfy the above equation except D

kilgo16 · Answer

Hey there,

Is there anything wrong with using S=An? According to this formula, we know that sum will always have to be divisible by 6, so look to see which number isn't divisible by 3 (since they're all even?).

Posted from my mobile device

KarishmaB · Answer

There is nothing wrong with using this formula.

Sum = Average * Number of terms

But note that you must first figure out that the average will be an integer so sum will be divisible by the number of terms i.e. 6.

Since there will be 6 numbers with a range of 10, the numbers will be like 1, 3, 5, 7, 9, 11 - i.e. alternate numbers. So average will be the number in the middle of 3rd and 4th numbers which will be an integer. Hence the sum will be divisible by 6.

NTA · Answer

"I don't understand the term "with a range of 10"..... can anyone plz help me to figure out that?

IanStewart · Answer

In Statistics, the "range" of a set is equal to the largest number in the set minus the smallest number in the set. So in this list, for example:

11, 23, 31, 73

the range is equal to 73 - 11, so the range is 62.

In the question in this thread, the range of the set is 10, so if S is the smallest number in the set, S + 10 will be the largest number.

Hope that helps!

rickyric395 · Answer

I used sum of AP here,
We know the formula for sum of terms in AP as SUM= n/2(2a+(n−1)d)

here n is number of terms i.e 6 here, a is initial number , d is common difference between terms.
SUM = 6/2(2a+5d)

since 2a+5d has to be integer, so options must be divisible by 3. and only option D is not divisible by 3. Hence D is the answer

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A department of motor vehicles asks visitors to draw numbered tickets

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