A 4-digit number '34PQ' is divisible by 3, 5 and 7. Find the value of P+Q.
- A11
- B12
- C10
- D13
Solution & Step-by-step Explanation
The 4-digit number 34PQ is divisible by 3, 5, and 7. Therefore, it must be divisible by their lowest common multiple (LCM).
LCM(3,5,7)=3×5×7=105
Let us find the range for the number 34PQ, which lies between 3400 and 3499.
Divide 3400 by 105:
105
3400
=32.38
The nearest multiples of 105 in this range are:
105×32=3360(less than 3400)
105×33=3465
Comparing 3465 with 34PQ, we get:
P=6andQ=5
Therefore, the value of P+Q is:
P+Q=6+5=11
LCM(3,5,7)=3×5×7=105
Let us find the range for the number 34PQ, which lies between 3400 and 3499.
Divide 3400 by 105:
105
3400
=32.38
The nearest multiples of 105 in this range are:
105×32=3360(less than 3400)
105×33=3465
Comparing 3465 with 34PQ, we get:
P=6andQ=5
Therefore, the value of P+Q is:
P+Q=6+5=11