# March 2019 (CML)

I will post seven new problems every weekend, one for each day of the week. The idea is that you work on your own during the week and I will post answers the following Saturday. For those of you who practiced with me last year, the process is similar.

For instructions on submitting weekly answers, click on the “Logistics” tab.
For previously posted problems, click on the “Archive” tab.
For previous prizes, click on the “News” tab.

Week of March 17 – March 23.

Click GoogleForm to submit answers by Sat, March 23.

March 17: $a\triangle b = {a \times b \over {a-b}}$. For example, $3\triangle 2 = {{3\times 2}\over {3-2}} = 6$. How much bigger is $16\triangle 8$ than $10 \triangle 5$?

March 18: During track practice, Al ran 3/5 of a mile, Bob ran 4/7 of a mile, Carl ran 1/2 a mile and Dan ran 2/3 of a mile. Who ran the furthest?

March 19: Tom was still 14 on Wed, Sept 9. Exactly 3 weeks ago his birthday was in 40 days. On what day of the week will Tom be 15 years old?

March 20: Tom was still 14 on Wed, Sept 9. Exactly 3 weeks ago his birthday was in 40 days. On what day of the week will Tom be 16 years old? (Assume no leap year is involved.)

March 21: How many multiples of 7 are between 15 and 95?

March 22: It takes 5 men 8 hours to build 10 shed. It would take 9 men ___ hours to build 45 sheds.

March 23: Which of the following is not the product of two prime numbers?
A) 55  B) 39  C) 91 D) 63  E) 65

Week of March 10 – March 16.

Click GoogleForm to submit answers by Sat, March 16.

March 10: $\sqrt{a}+\sqrt{b}+\sqrt{c}=20$. If $a = 49$ and $b= 16$, what is $c$?

Answer: c=81.

March 11: $\sqrt{{4\over 3}\cdot{5\over 4}\cdot {6\over 5}\cdot {7\over 6}\cdot {8\over 7}\cdot\dots \cdot {a\over{a-1}}}=2$. What is the value of $a$?

Answer: $\sqrt {a\over 3} = 2$. Therefore, a=12.

March 12: $0.004389\times\Box = 4389\times 39$. What is the number in the $\Box$?

Answer: 39000000

March 13: If ${a\over 3} = 4$ and ${b\over 4} = 24$, what is $a\over b$?

Answer: a=12, b=96. a/b = 1/8.

March 14: What is ${{100!-98!}\over 99!}$? Recall $n! =n\cdot (n-1)\cdot (n-2)\dots 3\cdot 2\cdot 1$.

Answer: $100-{1\over 99}$

March 15: If ${2\over 5} x ={3\over 5} y$, then ${3\over 5} x = \_\_\_ y$.

Answer: 9/10.

March 16: If $a\cdot b\cdot 7 = x$ and $a\cdot b =y$, then $x-y = k\cdot a\cdot b$. What is $k$?

Answer: k=6.

Week of March 3 – March 9.

Click GoogleForm to submit answers by Sat, March 9.

March 3: If $5 \times 7 = 19 + \Box$, what is the number that belongs in the box?

Answer: 16

March 4: If $4x^2 = 7$ and $5y^2=9$, what is $(10xy)^2$?

Answer: $(10xy)^2 = 5(4x^2)(5y^2)=5\cdot 7\cdot 9=315$.

March 5: 10 is 50% of 10% of what number?

Answer: 200

March 6: If $10(1^3+2^3+3^3+4^3) = m^3$, what is $m$?

Answer: $m^3 = 10(1+8+27+64)=1000$. So m=10.

March 7: If $_a F_b$ is defined as $b^a-a^b$, how much larger is $_5F_3$ than $_3F_5$?

Answer: $_5F_3- _3F_5 =(3^5-5^3) - (5^3-3^5)= 236$.

March 8: The average of 7 and x is equal to the average of 5, 9 and x. What is the value of x?

Answer: (7+x)/2 = (5+9+x)/3. Therefore, x=7.

March 9: If ${5\over 6} \cdot {9 \over A} = {1\over 2}$, what is $A$?

Answer: A=15.