### Author Topic: Test 2 solutions  (Read 4436 times)

#### yongcheng3315

• USAMO Winner
• Posts: 2585
##### Test 2 solutions
« on: January 21, 2014, 09:01:13 AM »
TEST 2
« Last Edit: January 21, 2014, 11:53:31 AM by yongcheng3315 »

#### ss5188

• 2012 AMC Summer Group
• Mathcounts Chapter Champion
• Posts: 16
##### Re: Test 2 solutions
« Reply #1 on: February 05, 2014, 10:38:06 PM »
For #28, could you explain in more details? I don't understand what the following means:
"Let the sum of the digits of a be 11x. Then the sum of the digits of b will be 11x + 1 + 1 –
9y = 11x + 2 – 9y (y is the number of carries of the sum of a and 11)."

For #29, I think you forgot to state that when both Alex and Bob increase their speed by 2km per hour, they'll meet in 6 hours.

#### yongcheng3315

• USAMO Winner
• Posts: 2585
##### Re: Test 2 solutions
« Reply #2 on: June 22, 2014, 06:46:27 AM »
29. Alex walks from village A and Bob walks from village B toward each other starting
at the same time. They meet in 8 hours. If each person increases the speed by 2 km per
hour, they will meet at the point 3 km away from the middle of the distance AB in 6
hours. What is Alex’s speed if he walks faster than Bob? Express your answer as a
decimal to the nearest tenth.