### Number Analogy Combined

Number Analogy - Concepts
Class - 8th ISO Subjects

Concept Explanation

## NUMBER ANALOGY

Analogy means correspondence.

Introduction  This section deals with two types of questions:

• Choosing a number related to a given number in the same manner as the two numbers of another given pair are related to each other.
• Choosing a similarly related pair as the given number pair on the basis of the relation between the numbers in each pair.
• Choosing a number similar to a group of numbers on the basis of certain common properties that they possess.
• Choosing a number set similar to a given number set.
• Example 1 : Find the missing term : 121 : 12 : : 25 : ?

(a) 1            (b) 2       (c) 6         (d) 7

Solution : (c) To find the missing term. Obtain the relationship as $\dpi{120} \fn_jvn \large x^{2}:(x+1)$. As 121 is the square of 11. By adding 1 we get 12. Similarly, we can use this relation for next term: 25 is the square of 5. so answer is 5 + 1 = 6

Example 2 : Find the missing term: 5 : 124 : :  7 : ?

(a) 125       (b) 248     (c) 342     (d) 343

Solution : (c) To find the missing term. Obtain the relationship as $\dpi{120} \fn_jvn \large x:(x^{3}-1).$. So, cube of 5 is 125. By subtracting 1 from 125, we get 124. Similarly, we can use this relation for next term: Cube of 7 is 343, By subtracting 1 , we get 342.

Example 3 : Find the missing term. 9 : 8 : : 16 : ?

(a) 27         (b) 18       (c) 17       (d) 14

Solution :   (a) To find the missing term. Obtain the relationship as $\dpi{120} \fn_jvn \large x^{y}:(x-1)^{y+1}$ . So, if we take x = 3, y=2,

$\dpi{120} \fn_jvn \large x^y=3^2=9$ and  $\dpi{120} \fn_jvn \large (x-1)^{y+1}=2^3=8$.

Similarly, we can use this relation for next term: $4^{2} = 16$, X = 4, Y = 2, X-1 = 4-1 = 3, Y+1 = 2+1 = 3 So, the answer is cube of 3 is 27.

Example 4 : Find the missing term: 16 : 27 :: 25 : ?

(a) 49     (b) 36     (c) 64   (d)  121

Solution : (c) In the given number analogy, first term is square of 4 and second term is cube of 3. Similarly, in case of third and fourth term. Third term is square of 5 and fourth term will be the cube of 4 is 64.

$x^{2} : (x-1)^{2+1}$

$4^{2} : (4-1)^{2+1}$

$16 : 27$

Similarly,

$x^{2} : (x-1)^{2+1}$

$5^{2} : (5-1)^{2+1}$

$25 : 64$

Example 5 : Select the pair in which the numbers are similarly related as in the given pair:     12 : 144

(a) 22 : 464          (b) 20 : 400       (c) 15 : 135      (d) 10 : 140

Solution: (d)  The relationship is $\dpi{120} \fn_jvn \large x:x^2$. So square of 12 is 144 and square of 20 is 400. So, correct answer is (b).

Example 6 :  Select the pair in which the numbers are similarly related as in the given pair: - 11 : 1210

(a) 6 : 216            (b) 7 : 1029       (c) 8 : 448        (d) 9 : 729

Solution : (c) The relationship is $\dpi{120} \fn_jvn \large x:(x^{3}-x^{^{2}}).$ So cube of 11 is 1331 and square of 11 is 121. 1331 - 121 = 1210. Similarly Cube of 8 is 512 and square of 8 is 64. 512 - 64 = 448. So option C is correct.

Example 7 : Complete the analogy: 144 : 23 :: 169: _____

(a) 34            (b) 42       (c) 24        (d) 25

Solution : So, its a tricky question. Lets start by analysing the relation between 144 and 23. So, 144 is square of 12, and number before 12 is 11. Adding 12 and 11 we get 23.

Similarly, apply this relation in next term: 169 is square of 13. and number before 13 is 12. Add 13 and 12 = 25. So option D is correct.

Sample Questions
(More Questions for each concept available in Login)
Question : 1
 In which of the following questions,choose one number which is similar to the numbers in the given set.Given set :992, 773, 845, 632 A.  114 B.  326 C.  425 D.  947 Right Option : C View Explanation
Question : 2
 Select the pair in which the number are similary related as in the given pair.64 : 16 : ? A.  216 : 81 B.  49 : 16 C.  216 : 36 D.  125 : 36 Right Option : C View Explanation
Question : 3
 Choose the best alternative            68 : 130 : : ? :350 A.  210 B.  216 C.  222 D.  240 Right Option : C View Explanation

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