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Set Question

Submitted by Incognito on Fri, 2007-09-14 02:22

A set S = { a, b, c, d } consists of prime numbers between 20 and 100, such that no two elements of S have any digit in common.

Q1. Which of the following statements is/are true?
I. No element of S is in the 70’s       
II. No element of S is in the 90’s    III. No element of S is in the 50’s

a. II and III alone
b. I and II alone

c. I and III alone
d. None of these
 
Q2. For which of the following ranges is it possible to obtain at least one distinct way of choosing the elements of S?
a. 30-80                  b. 40-90                c. 50-100                d. None of these

Q3. If the difference of some pairs of elements in S is prime, then find the largest possible value of a + b + c + d.

a. 190                     b. 232                   c. 250                    d. 272

 
Q4. Using the information provided in the above question, find the number of distinct ways in which the elements of S can be chosen. Assume that a > b > c > d ?
a. 14                     b. 288                   c. 8                        d. 336
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