Number Series Questions and Answers

Answer: D

The missing number is 14.

The series is two series interleaved. Taking every other term:

\[ \begin{aligned} &8,\ 11,\ \underline{\ \ },\ 17 \quad (+3) \\ &43,\ 41,\ 39 \quad (-2) \end{aligned} \]

The blank is the third term of the first series, \(11 + 3 = 14\), and the next term \(14 + 3 = 17\) confirms it. 8 and 43 repeat the first terms, and 44 would break both patterns.

In alternating series, it helps to split the terms by position (first, third, fifth and so on) whenever the numbers jump up and down instead of moving steadily.

Answer: A

The next number is 101.

Each term is 22 more than the one before: 35 - 13 = 22, 57 - 35 = 22 and 79 - 57 = 22. So the next term is \(79 + 22 = 101\).

The other options read the terms as pairs of digits and try to continue the digit pattern, but none of them is 22 more than 79, so they break the series.

Checking the difference between consecutive terms is always the first step with a number series; here it is constant, so the series is arithmetic.

Answer: A

The missing term is 122.

Each term is three times the previous one, minus 1.

\[ \begin{aligned} 2 \times 3 - 1 &= 5 \\ 5 \times 3 - 1 &= 14 \\ 14 \times 3 - 1 &= 41 \\ 41 \times 3 - 1 &= 122 \end{aligned} \]

The differences 3, 9, 27 confirm it: the next difference is 81, and \(41 + 81 = 122\). 124 would be \(41 \times 3 + 1\), the wrong sign.

Answer: C

There are three such 6's.

Go through every 6 in the series and check its neighbours:

• 2 6 3, 5 6 4 and 9 6 1: the 6 is preceded by 2 or 9, or followed by 4, so these fail.
• 1 6 3 (the 15th digit): preceded by 1, followed by 3, so it counts.
• 5 6 9 (the 20th digit): preceded by 5, followed by 9, so it counts.
• 1 6 5 and 9 6 7: followed by 5, or preceded by 9, so these fail.
• 1 6 3 at the end: preceded by 1, followed by 3, so it counts.

That gives three. Answers of one or two miss one of the qualifying 6's, and four counts one that fails a condition.

Answer: D

The missing number is 565.

Each term is the previous term multiplied by 1, 2, 3, 4 and so on, plus the same number:

\[ \begin{aligned} 2 \times 1 + 1 &= 3 \\ 3 \times 2 + 2 &= 8 \\ 8 \times 3 + 3 &= 27 \\ 27 \times 4 + 4 &= 112 \\ 112 \times 5 + 5 &= 565 \end{aligned} \]

452 is \(112 \times 4 + 4\), which repeats the previous step's multiplier instead of moving on to 5; 340 and 227 fit no step of the pattern.

Answer: C

The missing number is 42.

Each term is the product of two consecutive whole numbers:

\[ \begin{aligned} &1\times2,\ 2\times3,\ 3\times4, \\ &4\times5,\ 5\times6,\ 6\times7 \end{aligned} \]

which gives 2, 6, 12, 20, 30 and then 42. Equivalently, the differences rise by 2 each time: 4, 6, 8, 10, so the next difference is 12, and 30 + 12 = 42.

36 and 40 add too little (6 and 10) and 44 too much (14), so they break the pattern.