100 students appeared for two tests-Maths and English. For

[BTGmoderatorLU]

Source: e-GMAT

100 students appeared for two tests-Maths and English. For every student who passed in both the tests, 8 students passed only in Maths and 9 students passed only in English. How many students passed in neither Maths nor English?

1) More than 4 students passed in both the tests.
2) Less than 6 students passed in both the tests.

The OA is A

[GMATGuruNY]

Source: e-GMAT

100 students appeared for two tests-Maths and English. For every student who passed in both the tests, 8 students passed only in Maths and 9 students passed only in English. How many students passed in neither Maths nor English?

1) More than 4 students passed in both the tests.
2) Less than 6 students passed in both the tests.

100 = Only Math + Only English + Both + Neither

For every student who passed in both the tests, 8 students passed only in Maths and 9 students passed only in English.
Let B = both, implying that Only Math = 8B and that Only English = 9B.
Thus:
100 = 8B + 9B + B + Neither
100 = 18B + Neither
Neither = 100-18B

Statement 1:
Since Neither = 100-18B and B≥5, only B=5 is possible:
Neither = 100 - (18*5) = 100 - 90 = 10
SUFFICIENT.

Statement 2:
If B=5, then Neither = 10, as shown above.
If B≠5, then Neither ≠ 10.
Since Neither can be different values, INSUFFICIENT.

The correct answer is A.