If YE × ME = TTT, find the numerical value of Y + E + M + T.
If YE × ME = TTT, find the numerical value of Y + E + M + T.
Here, we have to find a number, where the three same digits come after multiplying such that the last digits of each number is the same.
In general form TTT can be expressed as:
⇒ 100T + 10 T + T = T(100 + 10 + 1)
⇒ 111T = (37 × 3)T
Thus, we can say that the value of TTT must be the multiple of 111.
The multiple of 111 will be:
⇒ 37 × 3 × 1 = 37 × 3 = 111
⇒ 37 × 3 × 2 = 37 × 6 = 222
⇒ 37 × 3 × 3 = 37 × 9 = 333
⇒ 37 × 3 × 4 = 37 × 12 = 444
⇒ 37 × 3 × 5 = 37 × 15 = 555
⇒ 37 × 3 × 6 = 37 × 18 = 666
⇒ 37 × 3 × 7 = 37 × 21 = 777
⇒ 37 × 3 × 8 = 37 ×24 = 888
⇒ 37 × 3 × 9 = 37 × 27 = 999
Since, ME × YE = TTT
Only possible case where the unit digit of two numbers is the same, is 37 × 27 = 999.
Hence, we can take 37 × 27 = 999
Thus, the values of M,Y, E and T will be 3, 2, 7, 9 or 2, 3, 7 and 9 respectively.
The numerical value of Y + E + M + T:
⇒ 2 + 3 + 7 + 9 or 3 + 2 + 7 + 9 = 21
Hence, the numerical value of Y + E + M + T will be 21.
Here, we have to find a number, where the three same digits come after multiplying such that the last digits of each number is the same.
In general form TTT can be expressed as:
⇒ 100T + 10 T + T = T(100 + 10 + 1)
⇒ 111T = (37 × 3)T
Thus, we can say that the value of TTT must be the multiple of 111.
The multiple of 111 will be:
⇒ 37 × 3 × 1 = 37 × 3 = 111
⇒ 37 × 3 × 2 = 37 × 6 = 222
⇒ 37 × 3 × 3 = 37 × 9 = 333
⇒ 37 × 3 × 4 = 37 × 12 = 444
⇒ 37 × 3 × 5 = 37 × 15 = 555
⇒ 37 × 3 × 6 = 37 × 18 = 666
⇒ 37 × 3 × 7 = 37 × 21 = 777
⇒ 37 × 3 × 8 = 37 ×24 = 888
⇒ 37 × 3 × 9 = 37 × 27 = 999
Since, ME × YE = TTT
Only possible case where the unit digit of two numbers is the same, is 37 × 27 = 999.
Hence, we can take 37 × 27 = 999
Thus, the values of M,Y, E and T will be 3, 2, 7, 9 or 2, 3, 7 and 9 respectively.
The numerical value of Y + E + M + T:
⇒ 2 + 3 + 7 + 9 or 3 + 2 + 7 + 9 = 21
Hence, the numerical value of Y + E + M + T will be 21.
