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:
Step-by-step explanation:
Incorrect point in question :- F is the greatest two-digit prime number
It is given that, Ram chose 6 different prime numbers and labeled them A, B, C, D, E and F.
1. F is the greatest two-digit prime number = 97
2. C - E = 1
∴ C = 3, E = 2
3. 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.
| A- F|=| D-A |
A=67, D=127
4. 4. F<B < D
97<B<127
→ B = 101, 103, 107, 109, 113
Step-by-step explanation:
Let the 6 different prime numbers be A, B, C, D, E, F
According to the condition (i)
F is the smallest 2-digit prime number and we know that smallest two digit prime number is 11.
Therefore F = 11
From condition (ii),
C - E = 1
And this is possible only in one case that is,
C will be 3 and E will be 2 since C > E
From condition (iii),
The distance between A and F is same as the distance between D and F.
Also A<D
Let say A = 5, F=11, D=17. This validates our condition.
According to condition (iv),
B > F and B < D.
In such case only one value of B is possible that is 13.
Hence A= 5, B= 13, C= 3, D=17, E = 2, F=11