Numbers/LCM/220815

Number N which when divided by 11, 9 & 8 gives 5, 6 and 7 as remainder respectively ?

A) find the small possible such number
B) find the largest 4 digit such number

Soln : 11 Q1 + 5 = 9.Q2 + 6 = 8.Q3 + 7
            60 + 55 Q4 = 8 Q3 + 7
         
           Smallest 159 , keep adding lcm of 11,8,9 for subsequent numbers

1303 : Arithmetic _CAT 2007

A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja.
giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise,
Shailaja noticed that she was left with exactly three times as much as the amount on the cheque.
Which of the following is a valid statement about the cheque amount?
(1) Over Rupees 13 but less than Rupees 14
(2) Over Rupees 7 but less than Rupees 8
(3) Over Rupees 22 but less than Rupees 23
(4) Over Rupees 18 but less than Rupees 19
(5) Over Rupees 4 but less than Rupees 5


Soln :

Suppose the cheque for Shailaja is of Rs. X and Y paise
As per the question: 3 × (100X + Y) = (100Y + X) – 50
⇒ 299X = 97Y – 50
⇒ Y = 299X + 50 /97

Now the value of Y should be a integer. Checking by options only for X = 18, Y is a integer and
the value of Y = 56

From Puneet Singh (www.bsaitmfbd.com) Eduventures