QUANT but CR Flashcards
Signal words indicate relationships to previous text
Why statement (1) Suff but not (2)
Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other’s point of departure. The two trains passed each other after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?
(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.
(2) Train Q averaged a speed of 55 miles per hour for the entire trip.
Attention to Detail: At the time when two trains passed, if we know exactly the average at point we can find the distance
(2) - Entire trip implies the unknown data point at the time two trains meet
Alt Strate beside Algebra
A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day?
(A) 2 mph (B) 3 mph(C) 4 mph(D) 5 mph(E) 6 mph
Avg Speed for whole trip: 64/18 = 3 + 10/18
The weighted average of 2 individual averages, r and r+1, must lie between these individual averages
- r < 3 + 5/9 < r+1 :only answer choice B fits.
After 5 games, a rugby team had an average of 28 points per game. In order to increase the average by n points, how many points must be scored in a 6th game?
Let’s say the team scored 28 points on the 6th game as well, the mean will not change. However we need the mean (average) to increase by n points. If the mean needs to be increased by n points, then the team should have 6n extra points in addition to the existing mean: 28 + 6n
Why you need to be careful about this problem?
If A = 2B, is A^4 > B^4?
(1) A^2 = 4B^2.
(2) 2A + B < A/2 + B.
There is no restriction of A &B, hence they can be any types of value: non-integers, pos/neg or equal to 0
A clothing manufacturer makes jackets that are wool or cotton or a combination of wool and cotton. The manufacturer has 3,000 pounds of wool and 2,000 pounds of cotton on hand. Is this enough wool and cotton to make at least 1,000 jackets?
(1) Each wool jacket requires 4 pounds of wool, and no cotton
(2) Each cotton jacket requires 6 pounds of cotton, and no wool
Attention to Detail: the question is asking about how many jackets in general, and not a specific type
When you see profit, unit & cost difference, what strategy can you use?
A grocer purchased a quantity of bananas at 3 pounds for $0.50 and sold the entire quantity at 4 pounds for $1.00. How many pounds did the grocer purchase if the profit from selling the bananas was $10.00?
profit amount difference/ Unit
Since we know the quantity must be divisible by 3 & 4, we can pick # of units as 12 -> Cost $2/12 lbs while Rev is $3/12 lbs —> $1 profit/ 12lbs. Therefore, $10 profit will have 120lbs
Why the answer is not 460/15 or 30? What is the hidden lesson?
A farmer decides to plant a row of trees along one side of a road. He decides to plant one tree every 15 metres. If the road is 460 metres long what is the maximum number of trees the farmer could plant?
C. 30
D. 31
If we divide 460 by 15 then the 1st tree will be on the 15 meter mark, leaving the potential starting point empty, of which we can plant the 1st tree instead
- This is the sequence test: A = {0, 15, 30, 45, 60 … 450}
- 450 = 0 + 15 (n-1) with n = number of trees
Use CR thinking mental math model w/o using equation
Company X has 50 employees and company Y has 60 employees. Both companies have same number of full time employees, but company Y has 3 more than twice the number of part-time employees that Company X has. How many part-time employees does Company Y have?
1) Since # of full-time between two companies are the same, the 10 extra employees difference (60-50) is accounted by the difference between part-time employees
2) 2 times P(X) + 3 - P(X) = 10 -> Part-time at Comp X = 7, then Comp Y has 2*7+3= 17
