Answer / guest

65292

As per given conditions, there are three possible
combinations for 2nd, 3rd and 4th digits. They are (3, 0, 7)
or (4, 1, 8) or (5, 2, 9)

It is given that there are 3 pairs whose sum is 11. All
possible pairs are (2, 9), (3, 8), (4, 7), (5, 6). Now
required number is 5 digit number and it contains 3 pairs of
11. So it must not be having 0 and 1 in it. Hence, the only
possible combination for 2nd, 3rd and 4th digits is (5, 2, 9)

Also, 1st digit is thrice the last digit. The possible
combinations are (3, 1), (6, 2) and (9, 3), out of which
only (6, 2) with (5, 2, 9) gives 3 pairs of 11. Hence, the
answer is 65292.

Answer / rajeswari

Step 1: Assign variables (x, y, z, a, b).
Step 2: Assign restrictions
x=3b
z=y-3
a=y+4

Assume that z+a is one of the pairs whose sum is 11.
y-3+y+4=11
2y+1=11
2y=10
y=5
z=2
a=9

Assume that x+y is one of the pairs whose sum is 11.
3b+5=11
3b=6
b=2
x=6

x=6
y=5
z=2
a=9
b=2

Check that three pairs equal 11. We already know that z+a=11 and x+y=11. Looking at our solutions we can also tell that a+b=11.

With all restrictions met, the 5 digit number is 65292.

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