CCAT Logical Reasoning: Number Series
Logical Reasoning: Number series
Here, a set of numbers, forming a sequence, will be given. The next number in the sequence will need to be figured out.
Q1:
2, 4, 6, 8, 10, ?
Answer:
Here, it is clear that each number is 2 more than its predecessor.
I.e. 4 = 2 + 2, 6 = 2 + 4, 8 = 2 + 6 etc
Hence, the next number will be 10 + 2 = 12
The way to solve these problems is to figure out the rules by which the sequence is formed. In the example above, the rule is: add 2 to each number to get the next number.
Some other popular rules are:
1. Add some fixed number to get the next number in the series. In the example above, this number was 2, but it could also be 3, 4, 5, 6 etc. For example:
2, 5, 8, 11, 14, ? (add 3, Answer: 17)
3, 8, 13, 18, 23, ? (add 5, Answer: 28)
4, 14, 24, 34, 44, ? (add 10, Answer: 54)
2. The difference between consecutive numbers keeps increasing (by 1, 2 etc). For example:
1, 2, 4, 7, 11, 16, ? (the differences are 1, 2, 3, 4 etc, Answer: 16 + 6 = 22)
2, 3, 5, 9, 17, 33, ? (the differences are 1, 2, 4, 8, 16 etc, Answer: 33 + 32 = 65)
3. Each number is the sum of the two previous numbers:
2, 4, 6, 10, 16, 26, ? (2+4=6, 4+6=10 etc, Answer: 16 + 26 = 42)
4. The sequence could be a combination of two different operations, performed alternately. For example:
1, 5, 3, 15, 13, 65 … ?
Here, we alternatively multiply by 5 and subtract 2:
1 * 5 = 5, 5–2 = 3, 3 * 5 = 15, 15–2 = 13 …. (Answer: 65–2 = 63)
5. Multiply each number by some number to get the next number:
1, 3, 9, 27, 81, …..?
(Here, each number is multiplied by 3 to get the next number, Answer: 81 * 3 = 243. This is also a special case of 6# below, using successive powers of 3)
6. Powers of numbers:
1, 4, 9, 16, 25 … ?
The numbers are 1*1, 2*2, 3*3, 4*4 etc, hence, the missing number is 6*6 = 36
Note: the * symbol denotes multiplication. (X is not used to avoid confusion with x, which is a common symbol for variables).
Now, try these:
Q-1: What would be the next number in the following series?
3 … 7 … 10 … 17 … 27 …?
Q-2: 31.8 What would be the next number in the following series?
2 … 4 … 6 … 10 … 16 … ?
Q-3: What would be the next number in the following series?
12 … 13 … 18 … 19 … 24 … 25 … ?
Q-4: What would be the next number in the following series?
0 … 3 … 8 … 15 … 24 … 35 … ?
Solutions:
Q-1: What would be the next number in the following series?
3 … 7 … 10 … 17 … 27 …?
Answer-1:
From the third term onward, each term is formed by adding together the two previous terms:
10 = 3 + 7
17 = 7 + 10
27 = 10 + 17
Hence, the next term will be formed by adding 17 + 27, which is 44.
Q-2: What would be the next number in the following series?
2 … 4 … 6 … 10 … 16 … ?
Answer-2:
The same logic as in Q-1 is followed. The answer = 10 + 16 = 26.
Q-3: What would be the next number in the following series?
12 … 13 … 18 … 19 … 24 … 25 … ?
Answer-3:
Let’s look at the difference between successive terms:
(13–12), (18–13), (19–18), (24–19), (25–24), which are
1, 5, 1, 5, 1 …..
Hence the next difference will be 5, and the next number will be 25 + 5 = 30.
Q-4: What would be the next number in the following series?
0 … 3 … 8 … 15 … 24 … 35 … ?
Answer-4:
Let’s look at the difference between successive terms:
(3–0), (8–3), (15–8), (24–15), (35–24), which are
3, 5, 7, 9, 11 ….
Following this pattern, the next difference will be 13, and the next term will be 35 + 11 = 46.
Coming up next: CCAT Logical Reasoning — Letter series
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