Ram chose 6 different prime numbers and labeled them A, B, C, D, E and F. He then asks his friend Sam to find these numbers using the following information.
(i)F is the smallest two-digit prime number.
(ii) C - E = 1
(iii) On the number line, the distance between A and F is the same as the distance between D and F. Also A is smaller than D.
(iv)B is greater than F and less than D.
Help Sam find these prime numbers. Enter the answers for the following questions in their respective boxes and then submit.
a.
(0.5 marks)
A is equal to _____ *
OK
Please fill this in
b.
(0.5 marks)
B is equal to ______ *
OK
Please fill this in
c.
(0.5 marks)
C is equal to ______ *
OK
Please fill this in
d.
(0.5 marks)
D is equal to ______
*
Answers
Answer:
Prime numbers chosen by Ram are
A = 5
B = 13
C = 3
D = 17
E = 2
F = 11
Step-by-step explanation:
We know that the list of prime numbers are as follows:
2,3,5,7,11,13,17,19,23,etc.,
(i) It is given that F is the smallest two-digit prime number. Therefore, F = 11
(ii) The only even prime number is '2' and two consecutive prime numbers with difference of one are 2 and 3. No other prime numbers have difference of one between them.
So, If C - E = 1 , then, C = 3 and E = 2.
(iii) A < D
F - A = D - F
11 - A = D - 11
=> D + A = 22
So, the prime numbers A and D must be below that value 22.
Also, A must be less than 11 and D must be greater than 11. Sum of A and D must be 22.
So, possible values are A = 5 and D = 17
( To cross check:
11 - 5 = 17 - 11
5 + 17 = 22 )
(iv) B > F and B < D
So, 11 < B < 17
Therefore, B = 13