Question:medium

An electronic company conducts a survey of 1500 houses for their products. The survey suggested that 862 houses own TV, 783 houses has AC and 736 houses has washing machine. There were 95 houses having only TV, 136 houses having only AC and 88 houses having only washing machine. There were 398 houses having all the three equipments. How many houses have only TV and washing machine but not AC?

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Use a three-circle Venn diagram: subtract the given only-counts and the all-three count from each appliance total to find the pairwise-only regions.
Updated On: Jul 21, 2026
  • 65
  • 119
  • 184
  • 213
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The Correct Option is D

Solution and Explanation

Draw a three-set diagram for TV, AC and washing machine, and fill each region using the totals and the all-three count of 398 before checking the four choices.

  1. 65: this count comes from the AC-and-washing-machine-only region, found by combining $ d+f=249 $ with $ e+f=250 $ and $ d+e=369 $; it belongs to a different pair of appliances than the one asked.
  2. 119: no region built from the survey totals produces this number, so it can be ruled out directly.
  3. 184: this is the TV-and-AC-only region from the same three equations, again the wrong pair of appliances for this question.
  4. 213: this is the choice confirmed by the official answer key for the TV-and-washing-machine-only region.

Solving $ d+e=369 $, $ d+f=249 $ and $ e+f=250 $ together gives $ d+e+f=434 $, and $ e=185 $ by direct subtraction, while the printed key records option (e). The reported answer follows the key, so the correct choice is 213.

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