Consider four-digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?
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Answers
Answered by
5
Answer:
The correct option is A.
Explanation:
Since first two and last two digits are equal, let the four-digit number be XXYY
This number can be expressed as:
1000X + 100X + 10Y + Y = 1100X + 11Y = 11(100X + Y) = k2 (perfect square)
In order for this to be true, 100X + Y must be the product of 11 and a perfect square, and looks like X0Y.
11 x 16 = 176; 11 x 25 = 275; 11 x 36 = 396; 11 x 49 = 593; 11 x 64 = 704; 11 x 81 = 891
The only one that fits is 704. This means there is only one four-digit number that works, and it is 7744.
Answered by
1
Answer:
The correct option is A.
Explanation:
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