CAT Number system Practice Problems Set 09

Question 1:
After the division of a number successively by 3, 4 and 7, the remainders obtained are 2, 1 and 4 respectively. What will be the remainder if 84 divides the same number?

[1] 80
[2] 75
[3] 41
[4] 53
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Question 2:
A boy is asked to put one mango in a basket when ordered 'One', one orange when ordered 'Two', one apple when ordered 'Three', and is asked to take out from the basket one mango and an orange when ordered 'Four'. A sequence of orders is given as: 1 2 3 3 2 1 4 2 3 1 4 2 2 3 3 1 4 1 1 3 2 3 4

How many total oranges were in the basket at the end of the above sequence?

[1] 1
[2] 4
[3] 3
[4] 2
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Question 3:
A boy is asked to put one mango in a basket when ordered 'One', one orange when ordered 'Two', one apple when ordered 'Three', and is asked to take out from the basket one mango and an orange when ordered 'Four'. A sequence of orders is given as: 1 2 3 3 2 1 4 2 3 1 4 2 2 3 3 1 4 1 1 3 2 3 4

How many total fruits will be in the basket at the end of the above order sequence?

[1] 9
[2] 8
[3] 11
[4] 10
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Question 4:
If u, v, w and m are natural numbers such that u^m+ v^m= w^m, then which one of the following is

true ?

[1] m ≥ min(u, v, w)
[2] m ≥ max(u, v, w)
[3] m < min(u, v, w)
[4] None of these
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Question 5:
\({7^{6n}}-{6^{6n}}\), where n is an integer > 0, is divisible by

[1] 13
[2] 127
[3] 559
[4] All of these
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