Difference between revisions of "2017 AMC 8 Problems/Problem 1"
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− | + | ==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 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. | ||
+ | |||
+ | |||
+ | 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 | ||
+ | |||
+ | ==See Also== | ||
+ | {{AMC8 box|year=2017|before=First Problem|num-a=2}} | ||
+ | |||
+ | {{MAA Notice}} |
Latest revision as of 18:45, 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.