Section 1- Critical Thinking and problem solving
Consider Z an integer such that 12<Z<22. Which of the following is the only option that could possible be the average of 2,8,12,17,23 and Z?
(12+62)=74< sum< (22+62)=84 74/6 and 84/6 = average
The front wheels of a toy have a circumference of 4cm. The back wheels have a circumference of 7cm. If the toy car travels in a straight line without slippage, how many centimetres will the toy car have travelldd when the front wheels have made 12 more revolutions than the back wheel
(N+12)x4 Nx7 7N=4(N+12) Solve for N. N=16
Out of 100 people in a group of tourists, 90 speak Italian, 80 speak Mandarin and 75 speak English. At least how many speak all three languages/
100-10-20-25=45
A shopper offers a loyalty discount card which costs £232 per year and gives an 8% discount on all purchases. How much willl a shopper have to buy before his discount covers the cost of the loyalty card.
232/0.08-£2900
If you divide 68 by a certain number X then the remainder is 4. What is the sum of all the possible values of X?
68-4=64. Numbers that multipy to make 64 and are greater than the number 4 are 8,16,32,64. Add these together and the answer is 120
In normal circumstances 6 similar ice cream making machines running simultaneously at a constant rate can complete a certain order in 8hrs. However today one of the machines is broken. If only 5 of these machines run at that rate how many more minutes will be required to complete the same order?
8/5=1.6=96minutes
Common Flaws
Absolute Numbers vs Percentages. Correlation vs Causation.Overlooking Alternatives. Illogical Comparisons. Projecting.Jumping to Conclusions.
What would be the equivalent to adding up 5 given numbers and then dividing the sum by 5.
Add the 5 numbers, doubling the sum and then moving the decimal point one place to the left
A school bus starts full with children. At each of its first 5 bus stops, it unloads half of the children present in the bus. After the 4th stop what proportion of the original busload of children is left on the bus.
After the first stop only half of the children will remain. After the second stop, a quarter of the children will remain. After the third stop, an eighth of the children will remain. After the fourth stop, one sixteenth of the children will remain so the answer is 1/16.
State the simplified, but accurate, way of viewing most BMAT passages
Arguments are made up of (1) a conclusion, (2) supporting reasons, and (3) unwritten assumptions.
7 common question types within Critical Thinking.
Conclusions, Assumptions, Flaws, Strengths & weaknesses, Inferences, Principles.
Car A and Car B started simultaneously from opposite ends of a straight 315 mile road and travelled towards each other without stopping until they passed each other at location X. The average speed of car B was 15mph higher than car A's. If car B's average speed is a third higher than car A's, how many miles of the road had car A travelled when the two cars passed each other.
Cr A's speed is 3x15 which is 45. Time therefore = distance over speed. Lets called distance X so. (X/45=315-X)60. Therefore 60X=45(315)-45X. This gives 105X=45x315. Rearrange to make X the subject and X =135
When driving to work Richard always sets off at the same time to start work at 9am. One day, he drove from home to work at a speed averaging 40 mph and arrived 12 minutes late. The next day he left home at the same time , took the same route, averaging 48 mph, and was 7 minutes late. What distance does he rive from home to work?
Distance=speed=time. We know the speed is 40 and 48 and we know how many minutes he was late by so we can write the following equation 40(t+12)/60=48(t+7)/60. The 60 cancels out. Expand the brackets then make the T the subject
On the medical student society committee, the number of females is one fewer than twice the number of males. Also if one female was replaced by one male member then there would be an equal number of males and females on the committee. How many members are there on the committee in total.
F=2M-1. M+1=F-1. F=M+2 M+2=2M-1. M=3 and F=5 so the answer is
At the train station train A leaves the station every 120 minutes, train B leaves the station every 140 minutes and train C leaves the station every 150 minutes. If during a given day the trains leave at the exact same instant, how many minutes will pass before the trains next leave the station simulataneosuly assuming the station runs constantly.
Find the lowest common multiple by using prime factorisation. Out of all the prime categories, 2,3,5, and 7 the highest powers from each category are 2 cubed , 3, 5 squared and 7. Multiply these numbers and this will give 2400minutes.
During a race on a straight line, greyhound A starts runnin straight away at a speed of 20m/s. Greyhound B is startled by the gunshot and only starts running after 10 seconds, but at a speed of 25m/s. Assuming both dogs run on the same racing line, at what distance from the starting line will greyhound B catch up with greyhound A
For dog A X=20T. For dog B X=25(T-10) 20T=25(T-10). Rearrange and solve for X
A group of 14 friends hired a bus to go from York to London for a weekend. The cost of the bus hire was shared quality amongst them. If there had been 20 passengers sharing the cost, the cost per passenger would have been £5 lower. What was each friend's share of the cost of hiring the bus?
If we call X the cost per passenger when split between 14 passengers, we can write the equation: 14X=20(X-5). Reaarange and solve for X
In a gold bullion store, the gold bricks are stacked up in a flat pyramid shape over a total of 6 rows. The number of bricks in a row s 1 less than the number of bricks in the row immediately below. If there are 105 gold bricks and 6 rows in total how many bricks does the bottom row contain?
Let N be the number of bricks in the bottom row. Since the row above has 1 bricks less than the bottom, it will contain N-1 bricks and the row above that will contain N-2 bricks. The equation can be written as follows. N+ (N-1)+(N-2)+(N-3)+(N-4)+(N-5)=105. Rearrange the equation making N the subject and the answer comes as 20
A rugby team has won 40% of the games it has already played if the team were to win 75% of its remaining games, it would have won 60% of all its games. How many remaining games are there?
Let Z be the number of games remaining (0.4 x 15) +(0.75 x Z)= 0.6 ( Z +15)
3 friends discuss their shopping experiences, comparing prices. All went shopping at the same time on the same day. Maria bought 1 pint of milk, 1 loaf of bread and 2 tomatoes for £3.50. Jenny bought 1 pint of milk and 3 tomatoes for £3.00. Robert bought a loaf of bread and 1 tomatoe for £1.50
Milk =M B=bread and T=tomatoe. Write equations for each purchase. Rearrange and solve
The general method for every critical thinking question is
Read the Question. Read the Argument. Discard & Decide
Method for long sets
Read the first question following the passage. Go back and read the passage, looking for the answer to question 1. Proceed.
How man zeros are there at the end of the number 100!
So the product of what numbers when multiplied ends in a zero: When one of the things being multiplied ends in zero itself. A number ending in 5 multiplied by an even number. 25, 50 and 75 when multiplied by some of the small numbers available eg (4, 2 and 6) generate an extra zero.
Consider the following T shape. If the shape's area is 324cm², what is its perimeter (in cm)?
The T shape is made up of 9 squares. Therefore the area of each square is 324/9=36. This means that one side of each square measures 6cm. The perimeter contains 20 sides and therefore measures 6x20=120
15 circles are arranged to form a rectangle measuring 3x5. A triangle is positioned on top of that pattern as shown below in such a way that's vertices are exactly in the centre of the circles which contain them. What is the area of the shaded triangle?
The diameter of a circle is 50/5=10cm. The base of the triangle spans 3 full circles and 2 half circles, i.e. a total of diameters i.e. 40cm. Similarly, the height of the triangle spans the equivalent of 2 diameters i.e 20 cms. The area of the triangle is bxhx0.5 and is therefore 40 x 20/2=400cm².
A safe has four dials. If the digit in each triangle is linked in some way to the three digits at the corners of each triangle, what digit should be entered in fourth position.
The pattern is as follows: Top digit-left hand digit x right hand digit. So answer for the last triangle is 6.
The rear wheels of a car cross a line 1 second after the front wheels have crossed the same line. If the wheels' axes of rotation are 5 metres apart, what is the speed of the car in kilometers per hour?
The speed of the car is 5 metres per second. To express this in km/h we need to multiply this by 3600 to convert to hours and divide by 1000 to convert to km. This gives 5 x 3.6 which =18.
A player throws a pair of normal dice 5 times in a row. Every time he records the products of the two numbers on each die. The score for the second roll is 5x more than that of the first the score for the third roll is 6 less than that of the second. The score for the 4th roll is 11 more than that of the third and the score for the 5th roll is eight less than that of the fourth
Throw 1; X Throw 2; X +5 Throw 3; X +5-6=X-1 Throw 4; (X-1) +11 = X+10 Throw 5; ( X+10)-8=X+2 Trial and error. X is 10 so the answer is that X ranges between 8 and 15.
You have bought a retangular bar of chocolate, which is made up of 10x6 indiviudal sqaures. How many steps are required to break the bar into individual squares? You can only cut along the pre made grooves and you cannot make stacks to break more than one peiece at a time.
When you break a piece of chocolate into two pieces, you are merely increasing the total number of pieces by 1. If we want to end up with 60 pieces we therefore need to break the chocolate tablet in 59 separate steps.
A computer shop sold 6 computers X and 4 Laptops Y for a total of £21,000. If each computer X was sold 50% less than each Laptop Y, how much did each computer X sell for?
Writing the question as an equation, we get; 6X + 4Y=21000. Since X=0.5Y we can substitute this into the original equation to solve for Y. 6(0.5Y)+4Y=21000. Y=21000/7=3000, thus X=1500
A tap can fill an empty bathtub with water in 30 minutes and the bathtubs sinkhole can empty a full tub in 40 minutes. The water flows at constant rates through both pipes regardless of the water level in the tub. If both the tap and the sinkhole were left open, what fraction of the tub would be filled exactly 1 hour after water began to flow into the empty tub?
X=volume of tub. In 1hr the tap can deliver 2X amount of water. In 1hr the sink hole can drain 1.5X of water. 2-1.5=0.5 so then after 1hr only half of the tub will be filled.
A year ago, Gary was twice as old as Ron is now . In 4 more years , Ron will be as old as Gary is now How old is Gary now?
if we call G and R Gary's and Ron's ages now, we can write the following equations: G-1=2R and R+4=G. Substituting G the equation goes as follows. R+4-1=2R. R then =3 and G =7
A salesman drives from A to B. The first half of the distance he drives at a constant speed of 80mp. The second half he drives at a constant speed of 120mph. What is his average speed for the total journey?
j= length of journey. First half j/2/80 which equals j/160. Do the same for the second half and you get j/240. j/(j160 + j/240). Factorise and then find a common denominator to add the fractions.
