OSSSC / OSSC MATH AND REASONING
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Ans. (c) :
The least number · (L.C.M of 15, 18, 36) x + 9 = 180x + 9
∵ (180x + 9) is divisible by 11.
∴ On taking x = 6,
Number · 180×6 + 9 = 1089 Sum of the digits of the number · 1+0+8+9 =18 ✅
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
What is the sum of the digits of the least number which when divided by 15, 18 and 36 leaves the same remainder 9 in each case and is divisible by 11?
Ans. (d) :
The number divisible by 5, 6 and 8 · (L.C.M of 5, 6 and 8)×k = 120 k
The numbers between 300 and 700 = (120×3), (120×4), (120×5) = 360, 480, 600
Hence, there are three numbers (360, 480, 600) between 300 and 700 which is divisible by 5, 6 and 8.
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
How many numbers between 300 and 700 are divisible by 5, 6 and 8?
Again the bells ring simultaneously after · (L.C.M of 3, 5, 8, 9 and 10)
= 360 seconds 360 / 60minutes
=6 minutes
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
Five bells ring together at the intervals of 3, 5, 8, 9 and 10 seconds. All the bells ring simultaneously at the same time. They will again ring simultaneously after:
Ans. (d) :
L.C.M of 12, 16, 18, 20 and 25 = 3600 ∴ x = 3600 k + 4
For k = 5, the number will be divisible by x = 7 x = 18004
Hence, the digit at the thousand's place will be 8.
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
When 12, 16, 18, 20 and 25 divide the least number x, the remainder in each case is 4 but x is divisible by 7. What is the digit at the thousands' place in x ?
Ans. (b) :
LCM of 5, 6 and 8 = 5 × 2 × 3 × 2 × 2 = 120
Required number · 120 + 3 = 123
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
Find the smallest number such that when it is divided by 5, 6 and 8 it leaves a remainder 3 in each case.
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
How many zeroes are there in product 4⁶ × 15¹⁰?
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
Find the positive number which when decreased by 20 is equal to 2925 times the reciprocal of the number.
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
If the difference between two numbers is 6 and the difference between their squares is 60, what is the sum of their cubes?
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
If A = 0.abcabc....., then by what number A should be multiplied so as to get an integeral value ?
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
How many numbers less than 350 are multiples of both 4 and 3?
