Sam uses different letters to represent different digits. He writes a number N as follows: ABABABABAB He notes that N when rounded off to the nearest: ten gives ABABABABBC hundred gives ABABABABCC thousand gives ABABABBCCC ten-thousand gives ABABABCCCC. . . . hundred-million gives ABCCCCCCCC billion gives BCCCCCCCCC Find N.
Answers
The number N is 4545454545.
- When N is rounded of to nearest ten ,the A at ten's place changes to B, so it is evident that B=A+1 because on rounding off the digit either remains same or increases by 1.
- We can also say that B>=5 because if it was not so the value at ten's place would not have increased on rounding off.
- On rounding of to nearest hundred the digit at hundred's place does not change,so the number AB must be less than 50.
⇒ 10×A + B < 50
⇒10×A + (A+1) <50
⇒A<49/11 or A<5
- On rounding off to nearest thousand the digit at thousand's place changes, so the number BAB must be greater than or equal to 500.
⇒100×B + 10×A + B >=500
⇒100×(A+1) + 10×A + (A+1) >=500
⇒A>=399/111 or A>3
- 3<A<5 and A is a number , so A must be equal to 4
- Subsequently, B=A+1⇒B=5
- Hence, the number N is 4545454545
Answer:
The number N is 4545454545.
When N is rounded of to nearest ten ,the A at ten's place changes to B, so it is evident that B=A+1 because on rounding off the digit either remains same or increases by 1.
We can also say that B>=5 because if it was not so the value at ten's place would not have increased on rounding off.
On rounding of to nearest hundred the digit at hundred's place does not change,so the number AB must be less than 50.
⇒ 10×A + B < 50
⇒10×A + (A+1) <50
⇒A<49/11 or A<5
On rounding off to nearest thousand the digit at thousand's place changes, so the number BAB must be greater than or equal to 500.
⇒100×B + 10×A + B >=500
⇒100×(A+1) + 10×A + (A+1) >=500
⇒A>=399/111 or A>3
3<A<5 and A is a number , so A must be equal to 4
Subsequently, B=A+1⇒B=5
Hence, the number N is 4545454545
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