Number series, missing-number and data sufficiency MCQ - Practice Questions with Answers

Elegant consistency in missing-number grids. A proposed rule should be tested on at least two complete rows or columns before applying it to the blank. If one row needs multiplication and another row needs addition, the rule is probably wrong unless the figure clearly signals a mixed system. Therefore, saying that one successful row is enough is incorrect. The average example with 6, 8, 10 and 12 is valid because their sum is 36 and 36 / 4 = 9.

Data sufficiency is about whether the statements fix one definite answer. From x + y = 10 alone, x can take many values because y is unknown. From y = 4 alone, x is not mentioned, so x is still not fixed. Taken together, y = 4 can be substituted in x + y = 10, giving x + 4 = 10 and hence x = 6. Both statements together are sufficient, while each alone is insufficient.

Mixed series often run as two independent sub-series, so alternate positions must be split before forcing one rule. The odd-position terms are 5, 8 and 11, increasing by 3 each time. The even-position terms are 20, 25 and 30, increasing by 5 each time. The blank is in the seventh position, an odd position, so it follows 5, 8, 11 and becomes 14.

One should check direct differences and then second-level differences when the first differences are not constant. Here the differences are 3, 5, 7 and 9. They are consecutive odd numbers, so the next difference should be 11. Adding 11 to 26 gives 37. The same series can also be read as square numbers plus 1: 1^2 + 1, 2^2 + 1, 3^2 + 1, 4^2 + 1 and 5^2 + 1, so the next term is 6^2 + 1 = 37.

Many missing-number traps come from operation order. In (4 + 5) x 3, the bracket is evaluated first, so 9 x 3 gives 27. In 4 + 5 x 3, multiplication is evaluated before addition, so 5 x 3 is 15 and 4 + 15 gives 19. The stated reason is therefore true and directly explains why the two expressions have different values.