Section A - Data Interpretation and Quantitative Ability

 

Question Nos. 35 – 36 are followed by two statements labelled as I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:

 

A.    Statement I alone is sufficient to answer the question.

B.    Statement II alone is sufficient to answer the question.

C.   Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.

D.   Either Statement I or Statement II alone is sufficient to answer the question.

E.    Neither Statement I nor Statement II is necessary to answer the question.

 

35.  Let PQRS be a quadrilateral. Two circles O1 and O2 are inscribed in triangles PQR and PSR respectively. Circle O1 touches PR at M and circle O2 touches PR at N. Find the length of MN.

I.     A circle is inscribed in the quadrilateral PQRS.

       II.    The radii of the circles O1 and O2 are 5 and 6 units respectively.

      

       Explanation:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

      

                    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In the first quadrilateral let PD = a, QD = b, RM = c, PA = d and SA = e

Now PA = PN + MN, QD = QC, RC = RN + RM, RM = RB and SA = SB

\ PS = d + e

SR = e + c

QR = b + c  + MN

PQ = a + b.

In the second quadrilateral,

PQ + SR = PS + QR

x1 + x4 + x2 + x3 = x1 + x2 + x3 + x4

\ a + b + e + c = d + e + b + c + MN.

a = d + MN

Þ a = a + MN + MN [∵ PM = PA]

Þ 2 MN = 0

Þ MN = 0.

Therefore the measure of MN can be answered from statement I alone.

Thus statement I alone is sufficient.

Statement II alone is not sufficient, for we can have more than one value of MN possible.                                                                                                                                        Choice (A)

      

36.  Given below is an equation where the letters represent digits.

       (PQ).(RQ) = XXX. Determine the sum of P + Q + R + X.

       I.     X = 9.

       II.    The digits are unique.

 

Explanation:

It is given that (PQ)(RQ) = XXX

There are 9 numbers of the form XXX

111 = 3 ´ 37 444 = 12 ´ 37             777 = 21 ´ 37

222 = 6 ´ 37 555 = 15 ´ 37             888 = 24 ´ 37

333 = 9 ´ 37 666 = 18 ´ 37             999 = 27 ´ 37

Only in 999, we get the unit’s digit of the two numbers the same. Since there is a unique value, so we need neither statement I nor statement II to answer the question.          Choice (E)