Algebra - Progressions - Previous Year CAT/MBA Questions
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Let Un+1 = 2Un + 1 (n = 0, 1, 2, ...) and u0 = 0. Then u10 is nearest to
- (a)
1023
- (b)
2047
- (c)
4095
- (d)
8195
Answer: Option A
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Text Explanation :
U0 = 0 = 20 – 1 = 0
U1 = 2 × 0 + 1 = 1 = 21 – 1
U2 = 2 × 1 + 1 = 3 = 22 – 1
U3 = 2 × 3 + 1 = 7 = 23 – 1 and so on.
⇒ Un = 2n - 1
∴ U10 = 210 – 1 = 1023.
Hence, option (a).
Workspace:
Let x < 0.50, 0 < y < 1, z > 1. Given a set of numbers, the middle number, when they are arranged in ascending order, is called the median. So the median of the numbers x, y, and z would be
- (a)
less than one
- (b)
between 0 and 1
- (c)
greater than 1
- (d)
cannot say
Answer: Option B
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Text Explanation :
Since there are two numbers which are less than 1 (viz. x and y), it is obvious that the median will be less than 1.
Hence, option (c) cannot be the answer.
Since x < 0.5 and 0 < y < 1, the median will not be less than 0.
Hence, option (b).
Workspace:
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