Difference between revisions of "2017 AMC 8 Problems/Problem 1"
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| − | ==Problem | + | ==Problem== |
Which of the following values is largest? | 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> | <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> | ||
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==Solution 1== | ==Solution 1== | ||
| − | We will compute each expression. A) <math>2+0+1+7=10</math> | + | We will compute each expression. |
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| + | A) <math>2 + 0 + 1 + 7 = 10</math> | ||
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| + | B) <math>2 \times 0 + 1 + 7 = 8</math> | ||
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| + | C) <math>2 + 0 \times 1 + 7 = 9</math> | ||
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| + | D) <math>2 + 0 + 1 \times 7 = 9</math> | ||
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| + | E) <math>2 \times 0 \times 1 \times 7 = 0</math> | ||
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| + | 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>. | ||
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| + | - SBose | ||
==Solution 2== | ==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{(A) 2+0+1+7}</math> is your answer. | + | 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. |
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| + | https://youtu.be/S1gAyiyQWYo | ||
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| + | ~Education, the Study of Everything | ||
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| + | ==Video Solution== | ||
| + | https://youtu.be/cY4NYSAD0vQ | ||
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| + | https://youtu.be/o5Aus-6w1vs | ||
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| + | ~savannahsolver | ||
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| + | https://youtu.be/S1gAyiyQWYo | ||
| + | |||
| + | ~Education, the Study of Everything | ||
==See Also== | ==See Also== | ||
Latest revision as of 17:45, 15 June 2024
Problem
Which of the following values is largest?
Solution 1
We will compute each expression.
A) 
B) 
C) 
D) 
E) 
Ordering these, we get 
. Out of these, 
is the largest number and option 
adds up to . Therefore, the answer is 
.
- SBose
Solution 2
We immediately see that every one of the choices, except for A and D, has a number multiplied by 
. This will only make the expression's value smaller. We are left with A and D, but in D, 
is multiplied by 
to get , whereas in answer choice A, we get 
out of and , instead of . Therefore, is your answer.
~Education, the Study of Everything
Video Solution
~savannahsolver
~Education, the Study of Everything
See Also
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
