Difference between revisions of "2021 AMC 10B Problems/Problem 5"

(Video Solution by TheBeautyofMath)
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==Problem==
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The ages of Jonie's four cousins are distinct single-digit positive integers. Two of the cousins' ages multiplied together give <math>24</math>, while the other two multiply to <math>30</math>. What is the sum of the ages of Jonie's four cousins?
 
The ages of Jonie's four cousins are distinct single-digit positive integers. Two of the cousins' ages multiplied together give <math>24</math>, while the other two multiply to <math>30</math>. What is the sum of the ages of Jonie's four cousins?
  
 
<math>\textbf{(A)} ~21 \qquad\textbf{(B)} ~22 \qquad\textbf{(C)} ~23 \qquad\textbf{(D)} ~24 \qquad\textbf{(E)} ~25</math>
 
<math>\textbf{(A)} ~21 \qquad\textbf{(B)} ~22 \qquad\textbf{(C)} ~23 \qquad\textbf{(D)} ~24 \qquad\textbf{(E)} ~25</math>
  
==Solution 1==
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==Solution==
  
 
First look at the two cousins' ages that multiply to <math>24</math>. Since the ages must be single-digit, the ages must either be <math>3 \text{ and } 8</math> or <math>4 \text{ and } 6.</math>
 
First look at the two cousins' ages that multiply to <math>24</math>. Since the ages must be single-digit, the ages must either be <math>3 \text{ and } 8</math> or <math>4 \text{ and } 6.</math>
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We are required to find the sum of the ages, which is <cmath>3 + 8 + 5 + 6 = \boxed{(B) \text{ } 22}.</cmath>
 
We are required to find the sum of the ages, which is <cmath>3 + 8 + 5 + 6 = \boxed{(B) \text{ } 22}.</cmath>
  
-PureSwag
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-[[User:PureSwag|PureSwag]]
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== Video Solution by OmegaLearn (Using Factors) ==
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https://youtu.be/oe7lnbDO8bo
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~ pi_is_3.14
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==Video Solution by TheBeautyofMath==
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https://youtu.be/gLahuINjRzU?t=857
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 +
~IceMatrix
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==Video Solution by Interstigation==
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https://youtu.be/DvpN56Ob6Zw?t=358
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~Interstigation
  
 
== See Also ==
 
== See Also ==
  
{{AMC10 box|year=2021|ab=B|before=Problem 4|num-a=6}}
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{{AMC10 box|year=2021|ab=B|num-b=4|num-a=6}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 01:05, 23 February 2021

Problem

The ages of Jonie's four cousins are distinct single-digit positive integers. Two of the cousins' ages multiplied together give $24$, while the other two multiply to $30$. What is the sum of the ages of Jonie's four cousins?

$\textbf{(A)} ~21 \qquad\textbf{(B)} ~22 \qquad\textbf{(C)} ~23 \qquad\textbf{(D)} ~24 \qquad\textbf{(E)} ~25$

Solution

First look at the two cousins' ages that multiply to $24$. Since the ages must be single-digit, the ages must either be $3 \text{ and } 8$ or $4 \text{ and } 6.$

Next, look at the two cousins' ages that multiply to $30$. Since the ages must be single-digit, the only ages that work are $5 \text{ and } 6.$ Remembering that all the ages must all be distinct, the only solution that works is when the ages are $3, 8$ and $5, 6$.

We are required to find the sum of the ages, which is \[3 + 8 + 5 + 6 = \boxed{(B) \text{ } 22}.\]

-PureSwag

Video Solution by OmegaLearn (Using Factors)

https://youtu.be/oe7lnbDO8bo

~ pi_is_3.14

Video Solution by TheBeautyofMath

https://youtu.be/gLahuINjRzU?t=857

~IceMatrix

Video Solution by Interstigation

https://youtu.be/DvpN56Ob6Zw?t=358

~Interstigation

See Also

2021 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
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 AMC 10 Problems and Solutions

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