Quant - Ratios Flashcards
What is Ratio ?
A ratio gives a measure of the relation between two quantities. It doesn’t give either of the two quantities. So score of A : score of B = 4:5 means that for every 4 points A scored, B scored 5 points.(It doesn’t mean that A actually scored 4 and B actually scored 5.) To get the actual points scored by the two of them, we would need one of the following (or one of many other) scenarios:
Scenario 1:
Given: A scored 40 points. How many points did B score?
Obviously 50, right? If A scored 10 times 4, B must have scored 10 times 5, right?
Scenario 2:
Given: A and B together scored 90 points. How many points did A score and how many did B score?
If I think in ratio terms, A and B scored 4 and 5 respectively i.e. 9 in all. But actually, they scored 90 in all i.e. 10 times 9. So A must have scored 10 times 4 = 40 and B must have scored 10 times 5 = 50.
Scenario 3:
Given: B scored 10 points more than A. How many points did A score?
B:A is 5:4. For 4 points of A, B scored 1 extra. If B actually scored 10 points more than A, A must have scored 10 times 4 i.e. 40 points (and B must have scored 50 points)
In each of the cases above, you can think of 10 as the common multiplier. It helps you arrive at all the actual values. When you multiply the numbers in ratio terms with the multiplier, you get the actual values. Let us look at another example.
A department manager distributed a number of books, calendars, and diaries among the staff in the department, with each staff member receiving x books, y calendars, and z diaries. How many staff members were in the department?
Statement 1: The numbers of books, calendars, and diaries that each staff member received were in the ratio 2:3:4, respectively.
Statement 2: The manager distributed a total of 18 books, 27 calendars, and 36 diaries.
Answer = E
https://www.veritasprep.com/blog/2016/02/ratios-gmat-data-sufficiency/
Two trains, A and B, traveling towards each other on parallel tracks, start simultaneously from opposite ends of a 250 mile route. A takes a total of 3 hours to reach the opposite end while B takes a total of 2 hours to reach the opposite end. When train A meets train B during the journey, how far is train A from its starting point?
Ans = 100
Since A takes 3 hours to travel the same distance for which B takes 2 hours, time taken by A and B is in the ratio 3:2 so their speeds must be in the ratio 2:3. Hence, A will cover 2/5th of the total distance of 250 miles and B will cover the rest of the (3/5)th of the total distance. Therefore, A will be 100 miles from its starting point when A and B meet.
Relation between Distance & Speed
Relation between Distance & Time
Relation between Speed & Time
1) . We say Distance varies directly with Time (when Speed is kept constant) and 2). Distance varies directly with Speed (when Time is kept constant)
3) . Speed varies inversely with Time (when Distance is kept constant).
The speed of bus A is 20% more than the speed of bus B. Bus B takes 2 hours longer than bus A to travel 600 miles. What is the speed of bus A?
Speed of bus A is 20% more than speed of bus B. This means that speed of bus A : speed of bus B is 120:100 i.e. 6:5. To travel the same distance, time taken by bus A: time taken by bus B will be 5:6. This difference of 1 in the ratio of time taken is actually given to be 2 hours. Hence, the multiplier is 2. Time taken by bus A to travel the 600 miles must be 52 = 10 hrs and time taken by bus B to travel the 600 miles must be 62 = 12 hrs.
Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction of the work will be done by Adam?
Answer = 12/47
Time taken by Paul : Time taken by Abdul : Time taken by Adam = 3:4:5
Rate of work must be inverse of time taken. But how do you take the inverse when you have a ratio of 3 quantities? Does it become 5:4:3? No. Actually it becomes 1/3 : 1/4 : 1/5 (I will explain the ‘why’ for this when I take variation)
Rate of Paul : Rate of Abdul : Rate of Adam = 13:14:1513:14:15
Let’s multiply this ratio by the LCM to convert it into integral form. The LCM of 3, 4 and 5 is 60.
Rate of Paul : Rate of Abdul : Rate of Adam =(13)∗60:(14)∗60:(15)∗60=20:15:12=(13)∗60:(14)∗60:(15)∗60=20:15:12 (I would like to remind you here that multiplying or dividing each term of a ratio by the same number does not alter the ratio)
So if the total work is 20+15+12 = 47 units, Adam will complete 12 units out of it. Hence the fraction of work done by Adam will be 12/47.
A certain brand of house paint must be purchased either in quarts at $12 each or in gallons at $18 each. A painter needs a 3-gallon mixture of the paint consisting of 3 parts blue and 2 parts white. What is the least amount of money needed to purchase sufficient quantities of the two colors to make the mixture?
(4 quarts = 1 gallon)
A. $54 B. $60 C. $66 D. $90 E. $144
ans = 66
Let B and W be the amounts of blue and white paints to be used, respectively.
1 qt = 0.25 gal
B:W:Total = 3:2:5
Total = 3 gal B = 3(3/5) = 9/5 = 1.8 gal W = 3-1.8 = 1.2 gal
The cheapest way is to buy 2 gallons of blue and 1 gallon and 1 quart of white paint.
3(18)+12 = $66
Miguel is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?
A. 15/29 B. 5/8 C. 5/16 D. 1/2 E. 13/27
Since this is a pure ratio problem, I’d probably find it easiest just to choose a convenient number for the amount of salad dressing we’re making. You could also work purely with fractions, though that’s a bit more awkward. Here, we know that 5/8 of the dressing is oil, 2/8 is vinegar, and the remaining 1/8 is an equal mixture (‘even’? they mean ‘equal’) of salt, pepper and sugar, so (1/3)(1/8) = 1/24 of the dressing is salt, 1/24 is sugar, and 1/24 is pepper. So we can suppose we would normally be making 24 units of the dressing. We then normally would have:
15 units of oil 6 units of vinegar 1 unit of sugar 1 unit of salt 1 unit of pepper
Now if we double the vinegar and omit the sugar we have
15 units of oil 12 units of vinegar 0 units of sugar 1 unit of salt 1 unit of pepper
for a total of 29 units, 15 of which are oil. So the answer is 15/29.
If you are asked to make proportional changes to a starting ratio, you can determine the resulting ratio without ever needing to know the actual values.
Say that there are a set of balloons of 3 different colors, and we know that the ratio of blue, green, and pink balloons is 3:4:5. If the GMAT testmakers asks us to double the number of blue balloons and halve the number of green balloons, we’d be fine.
Let’s take the blue:green:pink 3:4:5 balloon example above. What if the question was to determine the new ratio when we add 20 blue balloons to the mix?
Sorry — now we can’t do it!
Jack and Mark both received hourly wage increases of 6 percent. After the increases, Jack’ hourly wage was how many dollars per hour more than Mark’s?
(1) Before the wage increases, Jack’s hourly wage is $5 per hour more than Mark’s
(2) Before the wage increases, the ratio of the Jack’s hourly wage to Mark’s hourly wage is 4 to 3
(2) Before the wage increases, the ratio of the Jack’s hourly wage to Mark’s hourly wage is 4 to 3 –> just ratio is not enough to get the value of new difference, as for different hourly wages we’ll get different result: bigger the wages the bigger the difference will be. Not sufficient.
Q 11) Jalal weighs twice as much as Meena. Meena’s weight is 60% of Bahar’s weight. Dolly weighs 50% of Laila’s weight. Laila weighs 19% of Jalal’s weight. Who among these 5 persons weighs the least?
A) Bahar B) Dolly C) Jalal D) Laila E) Meena
Meena’s weight is 60% of Bahar’s weight
Let’s let Bahar’s weight = 100 kg
So, Meena’s weight = 60 kg
Jalal weighs twice as much as Meena.
Since Meena weight 60 kg (see above) then Jalal’s weight = 120 kg
Laila weighs 19% of Jala’s weight
Jalal’s weight = 120 kg
19% is very close to 20%
20% of 120 kg = 24 kg
So, 19% of 120 kg = a little less than 24 kg
So, Laila weighs a little less than 24 kg
NOTE: At this point, we can see that, Laila is the lightest (so far!)
Dolly weighs 50% of Laila’s weight.
So, Dolly weighs LESS THAN Laila.
So, Dolly must weigh the least
Answer: D
In a certain company, if 75% of the employees usually use a laptop, what percent of the employees usually use a PDA (Personal Digital Assistant)?
(1) 60% of the employees who usually use a laptop also use a PDA.
(2) 90% of the employees who usually use a PDA also use a laptop.
I initially thought from 2 that as it is 90%X I can get the total (0.9X + 0.1 X = 75) which is completely wrong as 0,9X cab only be 10
When we add the same positive integer to the numerator and the denominator of a positive fraction, the fraction increases if it is less than 1 (but remains less than 1) and decreases if it is more than 1 (but remains more than 1). That is, we can say, that the fraction is pulled toward 1 in both the cases.
When we subtract the same positive integer from the numerator and the denominator of a positive fraction, the fraction decreases further if it is less than 1 and increases further if it is more than 1. That is, we can say, that the fraction is pushed further away from 1 in both the cases. An assumption here is that the positive number subtracted is less than both the numerator and the denominator.
Question: Two positive integers that have a ratio of 3:5 are increased in a ratio of 1:1. Which of the following could be the resulting integers? (A) 3 and 5 (B) 5 and 13 (C) 21 and 30 (D) 34 and 68 (E) 75 and 45X§X
ans - C
So the answer option should lie between 3/5 and 1.
Dealership A and Dealership B both sell cars and trucks. If the ratio of cars to trucks each dealership sold in the last month is the same for both dealerships, did Dealership A sell the same number of cars and trucks last month?
(1) The number of trucks sold by Dealership B was three times the number of cars sold by Dealership A.
(2) The number of cars sold by Dealership B was equal to the number of trucks sold by Dealership A plus twice the number of cars sold by Dealership A.
Say A sells c cars and t trucks.
Ratio of cars:trucks = c:t
B sells cars:trucks in the ratio c:t too.
We need to find if c = t or if c/t = 1?
(1) The number of trucks sold by Dealership B was three times the number of cars sold by Dealership A.
Trucks sold by B = 3c
Not sufficient.
(2) The number of cars sold by Dealership B was equal to the number of trucks sold by Dealership A plus twice the number of cars sold by Dealership A.
Cars sold by B = t + 2c
Not sufficient.
Using both, (t + 2c)/3c = c/t (Ratio of cars/trucks for B)
t2+2ct=3c2t2+2ct=3c2
Divide by t^2 to get 3c2t2−2(ct)−1=03c2t2−2(ct)−1=0 (assume c/t = x)
3x2−2x−1=03x2−2x−1=0
(3x+1)(x−1)=0(3x+1)(x−1)=0
Since x cannot be negative (number of cars and trucks sold both must be positive), x = 1 i.e. c/t = 1
Sufficient. Answer (C)
A school supply store sells only one kind of desk and one kind of chair, at a uniform cost per desk or per chair. If the total cost of 3 desks and 1 chair is twice that of 1 desk and 3 chairs, then the total cost of 4 desks and 1 chair is how many times that of 1 desk and 4 chairs?
A. 5 B. 3 C. 8/3 D. 5/2 E. 7/3
Ans = E
