2017 AMC 8 Problems/Problem 1: Difference between revisions

Latest revision as of 17:55, 7 June 2025

Problem

Which of the following values is largest?

$\textbf{(A) }2+0+1+7\qquad\textbf{(B) }2 \times 0 +1+7\qquad\textbf{(C) }2+0 \times 1 + 7\qquad\textbf{(D) }2+0+1 \times 7\qquad\textbf{(E) }2 \times 0 \times 1 \times 7$

Solution 1

We will compute each expression.

A) $2 + 0 + 1 + 7 = 10$

B) $2 \times 0 + 1 + 7 = 8$

C) $2 + 0 \times 1 + 7 = 9$

D) $2 + 0 + 1 \times 7 = 9$

E) $2 \times 0 \times 1 \times 7 = 0$

Ordering these, we get $10, 8, 9, 9, 0$ . Out of these, $10$ is the largest number and option $(A)$ adds up to $10$ . Therefore, the answer is $\boxed{\textbf{(A) } 2+0+1+7}$ .

- SBose

Solution 2

We immediately see that every one of the choices, except for A and D, has a number multiplied by $0$ . This will only make the expression's value smaller. We are left with A and D, but in D, $1$ is multiplied by $7$ to get $7$ , whereas in answer choice A, we get $8$ out of $7$ and $1$ , instead of $7$ . Therefore, $\boxed{\textbf{(A) } 2+0+1+7}$ is your answer.

https://youtu.be/S1gAyiyQWYo

~Education, the Study of Everything

Video Solution

https://youtu.be/cY4NYSAD0vQ

https://youtu.be/o5Aus-6w1vs

~savannahsolver

https://youtu.be/S1gAyiyQWYo

~Education, the Study of Everything

2017 AMC 8 (Problems • Answer Key • Resources)
Preceded by First Problem	Followed by Problem 2
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: Unable to save thumbnail to destination

@@ Line 1: / Line 1: @@
-==Problem 1==
+==Problem==
 Which of the following values is largest?
 <math>\textbf{(A) }2+0+1+7\qquad\textbf{(B) }2 \times 0 +1+7\qquad\textbf{(C) }2+0 \times 1 + 7\qquad\textbf{(D) }2+0+1 \times 7\qquad\textbf{(E) }2 \times 0 \times 1 \times 7</math>
 ==Solution 1==
-We compute each expression individually according to the order of operations. We get <math>2 + 0 + 1 + 7 = 10</math>, <math>2 \times 0 + 1 + 7 = 8</math>, <math>2 + 0 \times 1 + 7 = 9</math>, <math>2 + 0 + 1 \times 7 = 9</math>, and <math>2 \times 0 \times 1 \times 7 = 0</math>. Since <math>10</math> is the greatest out of these numbers, <math>\boxed{\textbf{(A) }2+0+1+7}</math> is the answer.
+We will compute each expression.
+A) <math>2 + 0 + 1 + 7 = 10</math>
+B) <math>2 \times 0 + 1 + 7 = 8</math>
+C) <math>2 + 0 \times 1 + 7 = 9</math>
+D) <math>2 + 0 + 1 \times 7 = 9</math>
+E) <math>2 \times 0 \times 1 \times 7 = 0</math>
+Ordering these, we get <math>10, 8, 9, 9, 0</math>. Out of these, <math>10</math> is the largest number and option <math>(A)</math> adds up to <math>10</math>. Therefore, the answer is <math>\boxed{\textbf{(A) } 2+0+1+7}</math>.
+- SBose
+==Solution 2==
+We immediately see that every one of the choices, except for A and D, has a number multiplied by <math>0</math>. This will only make the expression's value smaller. We are left with A and D, but in D, <math>1</math> is multiplied by <math>7</math> to get <math>7</math>, whereas in answer choice A, we get <math>8</math> out of <math>7</math> and <math>1</math>, instead of <math>7</math>. Therefore, <math>\boxed{\textbf{(A) } 2+0+1+7}</math> is your answer.
-==Solution 1==
+https://youtu.be/S1gAyiyQWYo
-We immediately see that every one of the choices, except for A, has a number multiplied by <math>0</math>. This will only make the expression's value smaller. Therefore, <math>\boxed{\textbf{(A) }2+0+1+7}</math> is your answer
+~Education, the Study of Everything
+==Video Solution==
+https://youtu.be/cY4NYSAD0vQ
+https://youtu.be/o5Aus-6w1vs
+~savannahsolver
+https://youtu.be/S1gAyiyQWYo
+~Education, the Study of Everything
 ==See Also==
@@ Line 15: / Line 46: @@
 {{MAA Notice}}
+[[Category:Introductory Algebra Problems]]

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