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State whether the given statement is true or false.

The three rational numbers $2128, 2228, 2328$ lie between $57 and 67 .$

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True

False

answer is A.

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Detailed Solution

Here, we have to find whether the three rational numbers

2128, 2228, 2328

lie between

57 and 67

or not.
Multiply the numerator and denominator of

57

by 4.

∴ 57 = 57 × 44 = 2028

Multiply the numerator and denominator of

67

by 4.

∴ 67 = 67 × 44 = 2428

We know that,
20 < 21 < 22 < 23 < 24

⇒ 2028 < 2128 < 2228 < 2328 < 2428

Therefore, the three rational numbers

2128, 2228, 2328

lie between

57 and 67 .

Thus, the given statement is true.
Hence, option (1) is correct.

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