JIPMAT 2023 (QA) - Given below are two statements: Statement (I): The difference, the sum, and the product of two numbers are in the ratio 1: 5: 12. The product of the two numbers is 18.Statement (II): The last digit in the decimal representation of 291 is 6. In light of the above statements, choose the most appropriate answer from the options given below. | PYQs + Solutions

JIPMAT 2023

Number System

Miscellaneous

Easy

Given below are two statements:
Statement (I): The difference, the sum, and the product of two numbers are in the ratio 1: 5: 12. The product of the two numbers is 18.
Statement (II): The last digit in the decimal representation of 2⁹¹ is 6.
In light of the above statements, choose the most appropriate answer from the options given below.

Both Statement (I) and Statement (II) are true.

Both Statement (I) and Statement (II) are false.

Statement (I) is true but Statement (II) is false.

Statement (I) is false but Statement (II) is true.

Correct Option: 2

Let me solve this step by step:

Statement I:

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Let two numbers be x and y

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Given their difference:sum:product

= 1:5:12

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And product

= 18

So,

|x-y| : (x+y) : xy = 1:5:12

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Since

xy = 18

, and using ratios:

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|x-y| = \frac{18}{12} = \frac{3}{2}

x+y = \frac{18×5}{12} = \frac{15}{2}

From these equations:

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When

x > y

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x - y = \frac{3}{2}

and

x + y = \frac{15}{2}

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Solving gives

x = 4.5, y = 3

Numbers are not integers, Statement I is false.

Statement II:

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To find last digit of

2^{91}

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Pattern of last digit of powers of

2: 2,4,8,6,2,4,8,6...

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91

mod

4

3

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So last digit is

8

, not

6

Therefore Statement II is also false.