CAT Model Paper 6 Questions and Answers with Explanation Part 5
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Q: 23. In a triangle given below, Bisects at P. Also, is the median to the side . If the area of APR is 20 cm2, find the area of the quadrilateral.
Q 23 Find the Area of the Quadrilateral PRCQ
(A)
(B)
(C)
(D)
Ans: D
Solution:
The correct choice is (D).
Q 23 Area of the Quadrilateral PRCQ
To solve, draw a line
APR and AQS are similar. Given that (since P is the midpoint of AQ).
Hence, ratio of areas of and is
Hence, area of. Therefore area of quadrilateral
Since P is the midpoint of, area of area of. Let the area of and Q be ‘x’.
Hence area of
Since
Area of Eqn (1)
are similar. Hence,
Hence ratio of areas of and is .
(Area of = Area of area of quadrilateral)
Simplifying,
Area of
Hence Area of quadrilateral Area of quadrilateral
Q: 24. If p, q, r, s are positive numbers and find find the minimum value of
(A) 3
(B) 2
(C) 4
(D) Cannot be determined
Ans: C
Solution:
SOLUTION
The correct choice is (C).
The given expression can be simplified as follows:
Since the above equation can be rewritten as:
+
are positive, the minimum value of
and the minimum value of
is 2. Hence the minimum value of the expression is 4.
Q: 25. If a number n can be denoted as in a number system with base m where , find the number n when converted to decimal if m is the greatest single digit prime number
(A)
(B)
(C) 333
(D)
Ans: C
Solution:
The correct choice is (C). 7 when converted to decimal becomes .
Q: 26. If the roots of are squared, what will be the new equation with the roots?
(A)
(B)
(C)
(D)
Ans: D
Solution:
The correct choice is (D). (
The roots are
If they are squared, they become
The new equation will be
Which translates to
Q: 27. Manoj repays a loan in three annual instalments which decrease by 1,000 every
year. The initial amount he borrowed was at the rate of Find the second instalment
(A)
(B)
(C)
(D)
Ans: A
Solution:
The correct choice is (A). Let the instalments be .
End of 1st year, P becomes
End of 2nd year,
End of 3rd year
Therefore,
.