CAT 1991 — QA Question 55
Answer the following questions based on the information given below:
There were a hundred schools in a town. Of these, the number of schools having a play – ground was 30, and these schools had neither a library nor a laboratory. The number of schools having a laboratory alone was twice the number of those having a library only. The number of schools having a laboratory as well as a library was one fourth the number of those having a laboratory alone. The number of schools having either a laboratory or a library or both was 35.
Each of these items has a question followed by two statements. As the answer,
Type 1, If the question can be answered with the help of statement I alone,
Type 2, If the question can be answered with the help of statement II alone,
Type 3, If both the statement I and statement II are needed to answer the question, and
Type 4, If the question cannot be answered even with the help of both the statements.
What is the area under the line GHI – JKL in the given quadrilateral OPQR, knowing that all the small spaces are squares of the same area?
- Length ABCDEQ is greater than or equal to 60.
- Area OPQR is less than or equal to 1512.
Answer & solution
- A
1
- B
2
3
- D
4
Let length of the smaller square be x.
From statement I,Length of ABCDEQ = 10x ≥ 60
Therefore, x ≥ 6
From statement II, Area of rectangle OPQR = 42x2 ≤ 1512
⇒ x2 ≤ 36
∴ x ≤ 6
By combining results from statement I and II we have, x = 6
Now, area under the ling GHI-JKL can be found out using x.
Hence, 3.