How many different numbers are possible when 2 or more different

Question

How many different numbers are possible when 2 or more different numbers from the following set are added together?

{0.1, 0.01, 0.001, 0.0001, 0.00001}

(A) 10
(B) 24
(C) 25
(D) 26
(E) 32

MartyMurray · Accepted Answer

How many different numbers are possible when 2 or more different numbers from the following set are added together?

{0.1, 0.01, 0.001, 0.0001, 0.00001}

When numbers are added, the order in which they're added doesn't matter. So, to find the correct answer we need to find a number of combinations of numbers in the set.

Glancing at the numbers, we see that there are no duplicates. Also, because there are only five different numbers and each is just 1/10 of the next bigger number, there are no ways to create duplicate sums of the numbers regardless of how many of them are added together.

So, to find the answer, we just need to find the number of possible combinations of 2 or more of the numbers.

Number of combinations of 2 numbers out of 5:

(5 * 4)/2! = 10

Number of combinations of 3 numbers out of 5:

(5 * 4 * 3)/3! = 10

Number of combinations of 4 numbers out of 5:

(5 * 4 * 3 * 2)/4! = 5

Number of combinations of 5 numbers out of 5:

1

Total:

10 + 10 + 5 + 1 = 26

The correct answer is (D).

SaquibHGMATWhiz · Answer

Solution:

Since all the numbers in the given set are different, picking any 2 or 3 or 4 or 5 numbers out of it will yield a different sums 
 So, number of ways we can pick 2 numbers to find different sum  =5C2=10  
 Number of ways we can pick 3 numbers to find different sum  =5C3=10  
 Number of ways we can pick 4 numbers to find different sum  =5C4=5  
 Number of ways we can pick 5 numbers to find different sum  =5C5=1  
 Total  =10+10+5+1=26

Hence the right answer is    Option D

gmatophobia · Answer

A good question!

The list consists of 5 different numbers. The question requires us to find the number of possible values of the sum when 2 or more different numbers from the following set are added together. As the numbers in the list are distinct, the resultant sum will be unique for each combination.

We can reframe the question as "  In how many ways can at least two numbers be selected from a list of 5 numbers  "

For each number, we have two possible cases - either it can be selected or not selected.

Hence, for  5  numbers we can  2^5  possible cases.

However, among these  2^5  possible cases, we also have cases wherein only one number is selected or in which none is selected. As we need at least two numbers, we need to subtract these cases.

Number of ways in which only number is selected =  5 
 
 Number of ways in which no number is selected =  1

Total =  2^5 - (5+1) = 32 - 6 = 26

Option D

Archit3110 · Answer

5c2+5c3+5c4+5c5=26
Option D

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saynchalk · Answer

there are 5 numbers and they can add 2 or 3 or 4 or 5 of these numbers

= 5c2 +5c3 +5c4 + 5c5
= 10+10+5+1
= 26

bbb1923 · Answer

Total subsets: 32
Subsets with 0 elements: 1
Subsets with 1 element: 5
Subsets with 2 or more elements: 32 - 1 - 5 = 26

Therefore, there are 26 distinct sums possible when adding 2 or more different numbers from the given set.

ManishaPrepMinds · Answer

The set has 5 elements: {0.1, 0.01, 0.001, 0.0001, 0.00001}.  
  The problem allows choosing any subset with size 2, 3, 4, or 5.  
 All five numbers are different, and each one is exactly one‐tenth of the previous. Because each number is in a different decimal place (tenths, hundredths, thousandths, ...), no two different selections can add to the same total. So there are no duplicate sums. 
 Therefore, the number of different sums equals the number of ways to choose 2 or more items from 5. Count the combinations :
Choose 2: C(5,2) = 10
Choose 3: C(5,3) = 10
Choose 4: C(5,4) = 5
Choose 5: C(5,5) = 1
10 + 10 + 5 + 1 = 26

How many different numbers are possible when 2 or more different

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How many different numbers are possible when 2 or more different

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