In the year 222 B.C, 100 CAT aspirants appeared in CAT- (Common Admission Test for MBA in some prestigious institutions). They had to show their competency in all the following four areas viz-Maths, Data Interpretation (DI), Logical Reasoning (LR) and English. Each aspirant had qualified in at least one section.
The number of aspirants who had qualified in maths, LR, DI, and English is 55, 38, 22 and 50 respectively. The number of aspirants who had qualified Maths and English is 30. The number of aspirants who had qualified LR and English is 15. The number of aspirants who had qualified Maths and LR is 20. The number of aspirants who had qualified Maths, L.R, and English is 5. The number of aspirants who had qualified DI and LR is 5. The number of aspirants who had qualified DI and Maths is 5. The number of aspirants who had qualified DI maths LR is 5.
Find the number of aspirants who had qualified only in English.

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Solution

The correct option is D
10

$D I, LR, a n d Maths i s 5 i . e, I I I_{MLD} + I V_{MLDE} = 5$
$Let I I I_{MLD} be X and I V_{MLDE} be 5 - X$
$D I a n d M a t h s i s 5 i . e, I I_{M D} + I I I_{M D E} + I I I_{M L D} + I V_{M L D E} = 5$
$Therefore, I I_{M D} = I I I_{M D E} = 0$
$DI and LR is 5 i . e, I I_{LD} + I I I_{LDE} + I I I_{MLD} + I V_{MLDE} = 5$
$Therefore, I I_{LD} = I I I_{LDE} = 0$
$Maths, L R, and English is 5 i . e, I I I_{MLE} + I V_{MLDE} = 5$
$Therefore, I I I_{MLE} = X$
$Maths and LR is 20 i . e, I I_{ML} + I I I_{MLD} + I I I_{MLE} + I V_{MLDE} = 20$
$Therefore, I I_{ML} = 15 - X$
$LR and English is 20 i . e, I I_{LE} + I I I_{LDE} + I I I_{MLE} + I V_{MLDE} = 15$
$Therefore, I I_{LE} = 10$
$Maths and English is 30 i . e, I I_{ME} + I I I_{MLE} + I I I_{MDE} + I V_{MLDE} = 30$
$Therefore, I I_{ME} = 25$
$Let I I_{D E} be Y$
$Therefore, I_{M} = 10, I_{L} = 8, I_{D} = 17 - Y, a n d I_{E} = 10 - Y$
$I_{M} + I_{L} + I_{D} + I_{E} + I I_{ML} + I I_{LD} + I I_{DE} + I I_{ME} + I I_{MD} + I I_{LE} + I I I_{MLD} + I I I_{LDE} + I I I_{MLE} + I I I_{MDE} + I V_{MLDE} = 100$
$Y = I I_{D E} = 0$
$Therefore, I_{M} = 10, I_{L} = 8, I_{D} = 17, a n d I_{E} = 10$

The number of aspirants who had qualified only in English = 10.

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