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· started a discussion

· 1 Months ago

value of d (Question:636404.0)

why d i s 43 and not 41 ?

Question:
The average of 4 distinct prime numbers a, b, c, d is 35, where a < b <c < d. a and d are equidistant from 36 and b and c are equidistant from 34 and a, b are equidistant from 30 and c and d are equidistant from 40. The difference between a and d is:
Options:
A) 30
B) 14
C) 21
D) 28
Solution:
Ans: (b) Given that a < b < c < d


The only possible prime number between 30 and 34 is 31

Hence            b = 31, therefore a = 29

Similarly         c = 37     and        d =43

Therefore        d - a = 43 -29 = 14


Alternate solution-

As the average of the four prime numbers is 35.

a + b + c + d = 35 ยด 4 = 140.

Since a and d are equidistant from 36.

a + d = 72 .... (1)

Similarly, b + c = 68 .... (2)

a + b = 60 ... (3) and c + d = 80 ..... (4)

Using the equation (3) let us look for the prime values of a and b and the corresponding values of c and d using the equations 2 and 1.

Also given that a < b < c < d.

a

b

c

(68 - b)

d

(72 - a)

Remarks

7

53

15

65

c, d not prime

13

47

21

59

c not prime

17

43

25

55

c, d not prime

23

37

31

49

d not prime

29

31

37

43

Only possibility

\(\therefore\)(a, b, c, d) = 29, 31, 37, 43

\(\therefore\)d - a = 43 - 29 = 14    

Knowledge Expert

· commented

· 1 Months ago

Dear student
We have updated the alternate solution.
Please check it now.

Regards
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