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Giải Bài 2.62 trang 56 SGK Toán 6 Kết nối tri thức với cuộc sống tập 1

Bài toán cổ: Bác kia chăn vịt khác thường Buộc đi cho được chẵn hàng mới ra Hàng 2 xếp thấy chưa vừa Hàng 3 xếp vẫn còn thừa một con Hàng 4 xếp vẫn chưa tròn Hàng 5 xếp thiếu một con mới đầy Xếp thành hàng 7, đẹp thay Vịt bao nhiêu? Tính được ngay mới tài. (Biết số vịt chưa đến 200 con).

𓃲Tổng hợp đề thi học kì 2 lớp 6 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên...
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Đề bài

 Bác kia chăn vịt khác thường

Buộc đi cho được chẵn hàng mới ra Hàng 2 xếp thấy chưa vừa Hàng 3 xếp vẫn còn thừa một con Hàng 4 xếp vẫn chưa tròn Hàng 5 xếp thiếu một con mới đầy Xếp thành hàng 7, đẹp thay Vịt bao nhiêu? Tính được ngay mới tài. (Biết số vịt chưa đến 200 con).  

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Áp dụng các dấu hiệu chia hết cho 2, 3,4,7 để tìm được số vịt

Lời giải chi tiết

Gọi số vịt là x (\(x \in {\mathbb{N}^*},\,\,x < 200\)).Vì hàng 5 xếp thiếu 1 con nên x chia 5 dư 4=> x có chữ số tận cùng là 4 hoặc 9.Vì hàng 2, hàng 4 không xếp được, do đó x không chia hết được cho 2 và cho 4 .=> x có chữ số tận cùng là 9.Vì số vịt xếp được thành 7 hàng nên x\( \vdots \)7.Do đó x ∈ B(7), x có chữ số tận cùng là 9 và x < 200, nên x ∈ {49; 119; 189}.Mà x chia cho 3 dư 1 nên x = 49.Vậy có 49 con vịt.

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