Brain Busters V Quiz

Pencils at the ready for Brain Busters V……………….

1 What have these numbers in common apart from the fact that they are all odd : 121, 169, 225 ?

2 If John walks half as fast again as Mary, how far ahead will he be if they start together and John walks 180 yards ?

3 Fill in the missing figures in this sum : 1?9 x ? = 436

4 Two tanks six feet deep are filled with water. Two brass weights are held three feet above the surface, one above each tank. If both weights are 2 lbs, and the tanks are at temperatures 30 deg. Celsius and 30 deg. Fahrenheit respectively, and if both weights are released simultaneously, which weight will reach the bottom first ?

5 If 1.5 inches of rain fell on an acre and a half in one day, how much rain will have fallen on an acre ?

6 What is the sum minus the difference of two equal numbers that add up to ten ?

7 What is the sum of all the whole numbers from 1 to 100 (ie. 1+2+3………….97+98+99+100) ?

8 A man is due at a meeting to which he is going to walk. If he walks at 4mph he will be ten minutes late, but if he walks at 5mph he will be five minutes early. How far away is his meeting ?

9 What is the cube of four, times the cube of three, divided by the cube of two ?

10 A newspaper delivery boy has 30 Daily Bugles and 26 Daily Gazettes to deliver in a road of 50 houses. Five houses have no papers at all. How many have two ?

11 A farmer died, and in his will left one square mile of land to his four sons in proportion to their ages. How much land did the youngest get if the sons were aged 30, 25, 15 and 10 ?

12 What is 2 to the power of 8 ?

13 When does 59 equal 15 ?

14 A man has an appointment at 11am. He wants to be five minutes early. At the time, he thinks his watch is 25 minutes fast, but in fact it is 10 minutes slow. At what time does he arrive ?

Some of these are wicked, so points awarded will vary between 1,2 and 3 depending on difficulty. Good luck !

[H&J]

3. 109 x 4 = 436
5. 1.5 inches. either way it rained 1.5 inches
7. 5050

I'm impressed at the speed with which you worked those out, Jill.

3) was relatively easy, so 1pt.
5) was a slight trick question, you didn't make the obvious error, so 2pts.
7) was difficult, so 3pts. The quickest way to work it out is to take the numbers in pairs which add up to 101 (eg 1+100=101; 2+99 = 101; 3+98=101). There will be 50 such pairs, therefore the total is 50 x 101 = 5,050.

A "speed bonus" of 3 to add on.

Leader:
[glow=red,2,300]H&J 9pts[/glow]

[NigelS]

Ok H&J got there first but I will go for a point by showing the smart way of working 7) out

Sum of all numbers between 1 an 100

Rearrange sum so it is (1+100) + (2+99) + (3+98).......(50+51)
this equals 101 + 101 +101 + ... 101 or (50 x 101) = 5050

9) cube of 4 is 64, cube of 3 is 27, cube of 2 is 8

64 x 27 = 1,728
1,728/8 = 216

12) 2,4,8,16,32,64,128,256

So 2 to the power of 8 is 256

[NigelS]

14) 11.30 I think

Nigel proves he's no slouch either. ;)

7) You have shown the 'easy method' almost simultaneously so gain the 1pt requested.

9) 3pts earned for correct answer to question rated 'difficult', with workings.

12) Middle of the range question, 2pts for that one.

plus additional 2pts this time as a 'speed bonus'.

Leaderboard:
1 H&J 9pts
2 NigelS 8pts

nigels said:

14) 11.30 I think

Correct Nigel.
At 11.20 the man thinks his watch is 25 minutes fast, so he assumes that the time is 10.55. Since the watch is 10 minutes slow, the actual time is 11.30.
A good job he wasn't the AEBBA Tournament Director ! ;D I would imagine that a reliable timepiece would be a requisite of that job !

Now the points: difficulty rating was 3 so 3pts. Plus 1pt speed bonus as you did get your answer in just within the half-hour.

Leaderboard:
1 NigelS 12pts
2 H&J 9pts

[barbelman]

Tommo

Q1 They are the squares of 11, 13 and 15
Q2 60 yards assuming they walk in the same direction of course ;D
Q6 Ten!
Q11 Ooooarrr.......80 acres

cheers
Tony

[NigelS]

13) It is to do with temperature, got a Eureka moment when reading question 4, 15 degrees Celcius = 59 degrees Farenheit

Two more mathematicians......
Barbelman :
Q1 They are the squares of 11, 13 and 15 Indeed, all 'perfect squares'. 1pt
Q2 60 yards assuming they walk in the same direction of course Correct, 2pts
Q6 Ten! Correct, 2pts
Q11 Ooooarrr.......80 acres Correct. The proportion is 10: 30+25+15+10 (=80) Youngest son's share is one eighth of a square mile. 1 sq mile = 640 acres, so 80 acres is the right answer. 3pts

Nigel - your Eureka moment earns you 3pts for a non-obvious solution.

Leaderboard:
1 NigelS 15pts
2 H&J 9pts
3 Barbelman 8pts

[Q]

4. The 2nd tank....the weight will sink faster in a cooler temperature.

This was one of the 'wicked' questions, Bernie. ;D Normally I'd agree with you and your statement has some merit, so 1pt.
But the answer is 'the first tank' (the one at 30 degrees celsius).
Why ? Because the other tank is ice (freezing point for water = 32 degrees fahrenheit !)

Leaderboard:
1 NigelS 15pts
2 H&J 9pts
3 Barbelman 8pts
4 Q 1pt

'Fraid the rest of you aren't quick enough. ;D

The answer to 8) is Five miles away. If the distance was 1 mile, a (4mph) would take 15 minutes, b (5mph) would take 12 minutes: a difference of 3 minutes. So for a difference of 15 minutes, the distance must be 5 miles.

The answer to 10) is eleven. 56 papers are delivered to 45 houses, therefore (56-45=) 11 have both papers.

Quiz ended thus:
1 NigelS 15pts
2 H&J 9pts
3 Barbelman 8pts
4 Q 1pt