MOEMS Marathon

isabella2296

Rules:

1. Keep it MOEMS level.
2. When you answer, give a new problem. You can always make up one, or use Google.

Problem One:

Sally is thinking of a number. The product of the digits is one half of the number. What is the smallest positive, two-digit integer she could be thinking of?

**Posted:** Mon Jul 28, 2008 3:30 pm

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mz94

call the tens digit a and the ones digit b. then the numerical value is 10a+b

now we know that $ab = \frac{1}{2}(10a + b)$ so $2ab = 10a + b$ now we knwo b is even

the smallest number satisfying that is 36

new prob

find the hypontenuse of a triangle with legs 20 and 21

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isabella2296

We use the Pythagorean Theorem.

$20^2 + 21^2 = 841$

$\boxed{29}$

New Problem:

Similar to the first problem --

Randy wants to find the smallest, positive, two-digit integer which is twice the sum of its digits. What is it?

**Posted:** Mon Jul 28, 2008 3:40 pm

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mz94

this is easier. call the 2 digit number (once again) 10a+b. then the sum is a+b
10a+b=2(a+b). simplifying gives us 8a=b. the smallest number is therefore when a=1, b=8

18

new prob:

find the 2 digit number which is 120% the number that is formed when tis digits are reversed

**Posted:** Mon Jul 28, 2008 3:46 pm

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Oh, and just in case you didn't notice, Angie is my beeeest friend! =)

AIME15

45
i have no new probbbbbbbbbbbbbbbbbbb

**Posted:** Mon Jul 28, 2008 4:32 pm

FantasyLover

wth?? ernie's marathon got locked too??

let the 2 digit number be xy.

$xy=\frac{6}{5}yx$ .

$10x+y=\frac{6}{5}(10y+x)=12y+\frac{6}{5}x$

$\frac{44}{5}x=11y, x=5 y=4$

answer : 54

<New Problem>

What is the area of the triangle with side lengths 12, 16, and 20?

**Posted:** Mon Jul 28, 2008 4:35 pm

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Bachukas

**Posted:** Mon Jul 28, 2008 5:06 pm

mz94

**Posted:** Mon Jul 28, 2008 5:41 pm

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사랑해! 빅뱅>에픽하이!
Oh, and just in case you didn't notice, Angie is my beeeest friend! =)

Bachukas

**Posted:** Mon Jul 28, 2008 11:10 pm

isabella2296

These problems are getting a little too hard. I'll post an easier one, because I'd hate to get this locked.

Mr. Holmes buys a chair for $\$60$ . He tries to sell it for double the price, but when no one would buy it, he reduced that doubled price by $60\%$ . However, sales tax is $7\%$ . Including tax, what was the final price of the chair?

**Posted:** Tue Jul 29, 2008 3:39 am

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ernie

So, here's what you do.

$60 \cdot 2 = 120$

But since no one wanted to buy it at that price, we reduce it by 60%.

$120 \cdot 0.4 = 48$

Add tax.

$48 \cdot 1.07 = \boxed{51.36}$

Problem 9

**Posted:** Tue Jul 29, 2008 3:56 am

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isabella2296

Ernie, I believe that problem is too hard. Do you have another?

**Posted:** Tue Jul 29, 2008 4:03 am

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FantasyLover

meh, ill just solve it and post another problem.

ernie's - 7 and 24

<Problem 10>

Evaluate: $(3^4)^\frac{5}{4}$

**Posted:** Tue Jul 29, 2008 4:48 am

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heneieneh

THe fourth root of 3^4 cancels out to become 3. we then find 3^5 which is 243

**Posted:** Tue Jul 29, 2008 5:38 am

isabella2296

In the future, please post a second problem. Also, I suggest reading the rules in the first post.

New Problem:

[Taken from my blog] Compute the following without using a calculator: $\frac{8!}{6!2!}$ .

**Posted:** Tue Jul 29, 2008 5:44 am

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ernie

**Posted:** Tue Jul 29, 2008 5:48 am

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isabella2296

Let $x$ be the amount of money the tie costs, without tax.

$1.03x = 9.27$

$x = 9$

Thus, the tie costs $\$9$ .

If you take my age, double it, and add 1, you'll get the 9th prime number. How old am I?

**Posted:** Tue Jul 29, 2008 5:52 am

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ernie

**Posted:** Tue Jul 29, 2008 5:59 am

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If pro is the opposite of con, then what's the opposite of progress? Razz

isabella2296

Ernie, please post a solution. Mr. Green

**Posted:** Tue Jul 29, 2008 6:25 am

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levans

Problems are still too hard. You would never see a fractional exponent problem - a largely Algebra 2 topic - on a test geared for 4th through 8th graders.

**Posted:** Tue Jul 29, 2008 8:15 am