Dear Reader, Below are three questions requiring you to create and solve equations based on the data in questions.
Arun got a new mobile number. The first five digits are 99445. Find the next 5 digits, if the fourth digit from the right is twice the last digit from the left, the second digit from the left is two greater than the second digit from the right, the sum of last two digit from the left is same as the middle digit, the second digit from left is one less than third digit from the right and the second digit from the left is three times the first digit from the left?
a) 26734 b) 26752 c) 26743 d) 24752
Answer : c) 26743
Let the five digit be abcde.
From the question, we can infer that b = 2e, b = d+2, c = d+e, c = b+1 ( b = c - 1)and b = 3a.
Substitute c = d + e for c in c = b + 1 we get ,
d + e = b + 1
Now Substitute b = 2e we get,
d + e = 2e + 1
d - e = 1 ----------- eqn 1
Substitute b = 2e in b = 2 + d we get,
2e - d = 2 ------------ eqn 2
By Solving eqn 1 & 2 we get e = 3
Substituting e value we get,
d = 4, b = 6 , a = 3, c = 7
Hence the remaining 5 digits are 26743
Age of Kamal is a two digit number. If the sum of age and the reverse of his age is 110 and if the ten's digit is 4 less than the unit digit, then the age of Kamal is?
a) 73 b) 28 c) 82 d) 37
Answer : d) 37
Let the age of Kamal be 10a + b
Then the reversed age is 10b + a
Given that 10a + b + 10b + a = 110
11a + 11b = 110 ----- (1)
Also given that a = b – 4 ---- (2)
Solving (1) and (2), we get a = 3 and b = 7
So, the age of Kamal is 37
If a five digit number 526ab is divisible by 40, then find a and b.
a) 8, 0 b) 1, 6 c) 4, 0 d) 2, 0
Answer : c) 4, 0
L.C.M of 40 = 5 x 8
Since 526ab is divisible by 5 and 8, b = 0
And since 526a0 is divisible by 8, the last three digits must be divisible by 8.
i.e. 6a0 must be divisible by 8.
This will happen only when a = 4.
Hence, the last two digits are 4 and 0.