CAT Number system Practice Problems Set 07

Question 1:
In some code, letters a, b, c, d and e represent numbers 2, 4, 5, 6 and 10. We just do not know which letter represents which number. Consider the following relationships:

a + c = e,

b – d = d and

e + a = b

Which of the following statements is true?

[1] b = 4, d = 2
[2] a = 4, e = 6
[3] b = 6, e = 2
[4] a = 4, c = 6
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Question 2:
A change-making machine contains one-rupee, two-rupee and five-rupee coins. The total number of coins is 300. The amount is Rs. 960. If the numbers of one-rupee coins and two-rupee coins are interchanged, the value comes down by Rs. 40. The total number of five-rupee coins is

[1] 100
[2] 140
[3] 60
[4] 150
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Question 3:
Number S is obtained by squaring the sum of digits of a two-digit number D. If difference between S and D is 27, then the two-digit number D is

[1] 24
[2] 54
[3] 34
[4] 45
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Question 4:
The nth element of a series is represented as

X_n= (–1)ⁿX_n–1

If X₀= x and x > 0, then which of the following is always true?

[1] X_nis positive if n is even
[2] X_nis positive if n is odd
[3] X_nis negative if n is even
[4] None of these
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Question 5:
The owner of a local jewellery store hired three watchmen to guard his diamonds, but a thiefstill got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave of the diamonds he had then, and 2 more besides. He escaped with one diamond. How many did he steal originally?

[1] 40
[2] 36
[3] 25
[4] None of these
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