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41. Find the remainder when 65203 is divided by 7.
Note: We have manipulated the powers in the form of (4x + n). It means 203 is taken as,
203 = 4x + n = 4 × 50 + 3.
We neglect power which is in the multiple of 4.
Solution:
Note: We have manipulated the powers in the form of (4x + n). It means 203 is taken as,
203 = 4x + n = 4 × 50 + 3.
We neglect power which is in the multiple of 4.
44. Find unit digit of product (173)45 × (152)77 × (777)999.
Thus, Required remainder and unit digit will be 8.
Solution:
To find unit digit of a number or an Expression, We have to divide the number or expression by 10 and the remainder obtained by this operation would be the required unit digit.Thus, Required remainder and unit digit will be 8.
45. The square of a number greater than 1000 that is not divisible by three, when divided by three, leaves a remainder of
Solution:
In such cases remainder will always be 1.
46. If 146 Is divisible by 5n, and then find the maximum value of n.
Note:
We have taken integral value only, not the fractional.
For example = 29.2 but we have taken 29 and so on.
Solution:
Note:
We have taken integral value only, not the fractional.
For example = 29.2 but we have taken 29 and so on.
47. Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took of the mints, but returned four because she had a monetary pang of guilt. Fatima then took of what was left but returned three for similar reasons. Eswari then took half of the remainder but threw two back into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?
Solution:
48. Some birds settled on the branches of a tree. First, they sat one to a branch and there was one bird too many. Next they sat two to a branch and there was one branch too many. How many branches were there?
When they sat Two to a branch one branch was extra.
Now, we go through the options;
Checking option (A);
If there were 3 branches, there would be 4 birds.
(This would leave one bird without branch as per the question.)
When 4 birds would sit Two to a branch there would be one branch free
(as per the question.).
Hence, the option (A) is correct.
Solution:
When the birds sat one on a branch, there was one extra bird.When they sat Two to a branch one branch was extra.
Now, we go through the options;
Checking option (A);
If there were 3 branches, there would be 4 birds.
(This would leave one bird without branch as per the question.)
When 4 birds would sit Two to a branch there would be one branch free
(as per the question.).
Hence, the option (A) is correct.
49. If we divide the unknown two-digit number by the number consisting of the same digits written in the reverse order, we get 4 as quotient and 3 as remainder. If we divide the required number by sum of its digits, we get 8 as a quotient and 7 as a remainder. Find the number?
Checking option (C)
= 4 quotient and remainder 3.
= 8 quotient and remainder 7 as remainder.
Solution:
We go through the options,Checking option (C)
= 4 quotient and remainder 3.
= 8 quotient and remainder 7 as remainder.
50. The last three-digits of the multiplication 12345 × 54321 will be
345 × 321 = 110745
So, the last three digits are 745
Solution:
If we multiply the last three digits of each terms we get the last three digits.345 × 321 = 110745
So, the last three digits are 745