How many different sums can be formed when selecting one number from

Question

Set A={12, 13, 14, 15, 16}

Set B={13, 14, 15, 16, 17}

How many different sums can be formed when selecting one number from each set and added together?

A. 9
B. 10
C. 11
D. 12
E. 13

hrusher · Answer

Select 12 from Set A, there can be 5 cases (12+13, 12+14, 12+15, 12+16, 12+17)
Select 13 from Set A, there can be 1 case ( 13+17)
Select 14 from Set A, there can be 1 case ( 14+17)
Select 15 from Set A, there can be 1 case ( 15+17)
Select 16 from Set A, there can be 1 case ( 16+17)

These can be the only 9 cases.

gmatophobia · Answer

To Simplify the calculations, we can reduce the sets to take the distance from 12.

A_1  = {0,1,2,3,4}
 B_1  = {1,2,3,4,5}

0 => {1,2,3,4,5} |  All the numbers can be added, because 0 is the first number of  A_1

1 => {5} |  Starting second number of  A_1 , only the last digit of  B_1  needs to be added because the other differences have already been added above.

2 => {5}

3 => {5}

4 => {5}

Total possible sum = 9

Option A

Khaisev · Answer

What would answer be if *product* instead of *sum* was asked?
Also, is there are general formula to do such qs, especially to remove or count the duplicate sums or products that result?

Posted from my mobile device

mayankkamal999 · Answer

Was having trouble creating combinations for this. 
 I really liked the following approach for this question-

Smallest Sum:  The smallest number from Set A is 12. The smallest number from Set B is 13. Smallest sum = 12 + 13 = 25
 Largest Sum:  The largest number from Set A is 16. The largest number from Set B is 17. Largest sum = 16 + 17 = 33
 Consider Consecutive Integers: 
 
 Set A has consecutive integers. 
 Set B has consecutive integers. 
 When we add two sets of consecutive integers, the resulting sums will also be consecutive integers.  
 Count the Number of Sums:  The sums will range from 25 to 33, inclusive. Number of sums = 33 - 25 + 1 = 8 + 1 = 9

ettenetur · Answer

Note that numbers 13, 14, 15 and 16 are common in both the sets.”12” is unique to set 1 “17” is unique to set 2.
Picking 2 numbers from set 1 can be done in 5C2 ways
Excluding 12, Picking 2 numbers from 4 numbers in set 1 can be done in 4C2 ways.
The difference is 10 - 6 = 4 (4 unique numbers because of 12)

Repeat this for set 2 and you’ll get 4 more unique numbers

When 12 and 17 are added, we can 1 additional unique number.

Total = 4+4+1 =9 9 Ways Option A

How many different sums can be formed when selecting one number from

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How many different sums can be formed when selecting one number from

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