Representation of numbers in base 10 AMC 8 2013 , problem number 13
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and 
that is total score of Clara is ab .
[/et_pb_tab][et_pb_tab title="Hint 2" _builder_version="4.1" hover_enabled="0"]Now we know that any number in base 10 can be represented as ab=10 a+ b. Given, when Clara totaled her scores, she inadvertently reversed the units digit and the tens digit of one score. So, Clara misinterpreted ab as ba . Again , ba= 10b+a .
[/et_pb_tab][et_pb_tab title="Hint 3" _builder_version="4.1" hover_enabled="0"]The difference between the two is 
which factors into 
.So, what can we say from here?
[/et_pb_tab][et_pb_tab title="Hint 4" _builder_version="4.1" hover_enabled="0"]Therefore, since the difference is a multiple of 9, the only answer choice that is a multiple of 9 that is 45.
[/et_pb_tab][/et_pb_tabs][et_pb_text _builder_version="3.27.4" text_font="Raleway|300|||||||" text_text_color="#ffffff" header_font="Raleway|300|||||||" header_text_color="#e2e2e2" background_color="#0c71c3" min_height="12px" custom_margin="50px||50px" custom_padding="20px|20px|20px|20px" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3"]Cheenta AMC Training Camp consists of live group and one on one classes, 24/7 doubt clearing and continuous problem solving streams.[/et_pb_blurb][et_pb_button button_url="https://cheenta.com/amc-8-american-mathematics-competition/" url_new_window="on" button_text="Learn More" button_alignment="center" _builder_version="4.0.9" custom_button="on" button_bg_color="#0c71c3" button_border_color="#0c71c3" button_border_radius="0px" button_font="Raleway||||||||" button_icon="%%3%%" background_layout="dark" button_text_shadow_style="preset1" box_shadow_style="preset1" box_shadow_color="#0c71c3"][/et_pb_button][et_pb_text _builder_version="3.27.4" text_font="Raleway|300|||||||" text_text_color="#ffffff" header_font="Raleway|300|||||||" header_text_color="#e2e2e2" background_color="#0c71c3" custom_margin="50px||50px" custom_padding="20px|20px|20px|20px" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3"]
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