Thread: Worded problems.

Hi, I'm new to the forums and not sure if this post is in the right forum.

I have in total 10 questions that are absolutely doing my head in. If anyone could help me out and show me how to work these out, it'd be much appreciated.

1) In a class of 45 girls, all of whom have chosen to study either history or psychology, or both, 40 are studying psychology and 25 are studying history. How many are studying both?
A.12 B.20 C.22 D.14 E.8

2) A horse breeder owns 25 horses. If there are twice as many black horses as chestnuts, but the number of brown horses is one more than black and chestnut horses together, how many black horses are there?
A.8 B.12 C.9 D.6 E.10

3) A planes compass is upset by a storm so that the needle which should point north now points to the west. If the pilot flies south by his compass what is his true direction?
A.North B.South-West C.East D.West E.North West

4) In a bag of fruit I have as many oranges as apples and twice as many mandarines as oranges. If I have 15 pieces of fruit how many mandarines do I have?
A.6 B.8 C.2 D.7 E.4

5) A factory employed 120 men. If 25% of those were retrenched and 20% of those who remained were retrained for new jobs within the factory, how many men remained at their original job?
A.72 B.45 C.48 D.20 E.66

6) Two trains, X and Y, leave their common origin together on a 1200km trip. Train X travels three times slower than Y. How far has X to go when Y reaches its destination?
A.300km B.600km C.900km D.800km E.100km

7) I have a bag of oranges and bananas but 20% are bad. If there are 10 pieces of rotten fruit and there are 25 good oranges, how many good bananas are there?
A.15 B.20 C.25 D.30 E.35

8) In a class one-third of the students do psychology, two-fifths do economics and the remaining 8 do physics. How many students are there in the class?
A.12 B.30 C.18 D.24 E.16

9) In a garden, one-quarter of the trees are apple trees and one-third are orange trees. The remaining trees are lemons, grown as wind shelter. What is the number of apple trees in the garden?
A.1 B.2 C.3 D.4 E.5

10) In a crowded bus, five-eigths of the people had seats. Two-thirds of the remainder held straps to support them and the other 2 people had to use the seat back for support. How many people were on the bus?
A.15 B.12 C.16 D.24 E.10

Any help would be very much appreciated, thanks

1. It appears that there are 45 girls and every one of them must be studying at least one subject. If every one of them studied exactly one subject, the sum of those studying history and psychology would be 45. But it's 65, impling that 20 (65-45) are studying both.

2. Algebra.
C = Number of chestnuts,
2C = Number of black horses (twice as many),
C+2C+1 = Number of brown horses (one more than the sum of the other two)
Since there are 25 altogether, 25 = C+2C+C+2C+1. Solve for C and double it to derive the number of black horses.

3. Everything would appear to be shifted counterclockwise by the same amount. So if North is 12 o'clock, west is 9 o'clock, south is 6 o'clock...you can probably figure out the rest.

4. Algebra again.
A = apples
A = oranges (same number as apples)
2A = mandarins (twice as many as oranges)
A+A+2A = 15 (Are you sure that's not 16?)

The rest of these seem to be similar themed problems. Try the above approach of defining one unknown item as a letter of the alphabet and synchronizing the other items to it, as shown above. As you can see from the above, it should work.

I hope this helps.

- Steve