At a technology company, a team of 60 software engineers works on product development. Of … — GMAT

At a technology company, a team of $60$ software engineers works on product development. Of these engineers, $35$ work on the mobile application, $28$ work on the web platform, and $10$ work on neither project. How many engineers work on both the mobile application and the web platform?

A
$3$
$13$ Answer
C
$18$
D
$25$
E
$63$

Answer

13 engineers work on both the mobile application and the web platform.

According to the fundamental principle of overlapping sets for two groups, the total number of individuals in the universe is equal to the number of individuals in Group A plus the number in Group B, minus those counted in both groups (to prevent double counting), plus those in neither group:

\text{Total} = \text{Set A} + \text{Set B} - \text{Both} + \text{Neither}

. Substituting the given values gives

60 = 35 + 28 - \text{Both} + 10

. Simplifying the right side yields

60 = 73 - \text{Both}

, so

\text{Both} = 13

. Thus, the value

13

is correct.

Step-by-Step Solution

Identify the given set values and formula

\text{Total} = 60

\text{Mobile} = 35

\text{Web} = 28

\text{Neither} = 10

Define all components of the standard two-set overlapping formula:

\text{Total} = \text{Set A} + \text{Set B} - \text{Both} + \text{Neither}

Substitute the values into the overlapping sets formula

60 = 35 + 28 - \text{Both} + 10

Set up the linear equation to solve for the unknown intersection (Both).

Simplify and solve for Both

60 = 73 - \text{Both} \implies \text{Both} = 73 - 60 = 13

Combine like terms (

35 + 28 + 10 = 73

) and isolate the variable to find the number of engineers in both groups.

Key Concept

Two-Set Overlapping Venn Diagram Principle

Estimated Time:1m 0s

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