mathewhe/aqua_rat huggingface dataset:
Question: There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability that the number of men is equal to that of women?
(A) 18/35
(B) 16/35
(C) 14/35
(D) 13/35
(E) 12/35
Rationale: men= women means 2 men 2 women
total such combinations = 4c2 * 4c2 = 4!/2!.2! * 4!/2!.2! = 6*6
total combinations = 8c4 = 8*7*6*5/4*3*2*1 = 70
so probability = 36/70 = 18/35
hence A
Answer: (A) 18/35
Question: The diagonals of a rhombus are 15 cm and 12 cm. Find its area?
(A) 70
(B) 90
(C) 60
(D) 80
(E) 292
Rationale: 1/2 * 15 * 12
= 90
Answer:B
Answer: (B) 90
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
(A) 6
(B) 8
(C) 4
(D) 9
(E) 3
Rationale: S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6
Answer: A
Answer: (A) 6
Question: If 45-[28-{37-(15-*)}]= 59, then * is equal to:
(A) -29
(B) -19
(C) 20
(D) 29
(E) 39
Rationale: 45-[28-{37-(15-*)}]= 59 => 45-[28-{37-15+*}]=59
45-[28-37+15-*]=59 => 45[43-37-*]=59
45-[6-*]=59 => 45-6+*=59
39+*=59 => *=59-39
= 20
ANSWER:C
Answer: (C) 20
Question: A sum of money lent out at S.I. amounts to Rs. 820 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is?
(A) Rs.440
(B) Rs. 500
(C) Rs. 540
(D) Rs. 740
(E) Rs. 840
Rationale: S.I for 5 years = (1020 - 820) = Rs. 200.
S.I. for 2 years = 200/5 * 2 = Rs. 80.
Principal = (820 - 80) = Rs. 740.
ANSWER:D
Answer: (D) Rs. 740
Question: At a contest with 2000 participants, 1/2 of the people are aged 16 to 18. Next year, the number of people aged 16 to 18 will increase by 1/4. After this change, what percentage of the total 2000 people will the 16- to 18- year-olds represent?
(A) 62.50%
(B) 60%
(C) 70%
(D) 65%
(E) 66/3%
Rationale: I just wanted to mention a couple of things here:
* this is a pure ratio question; the number 2000 is completely irrelevant, and you can ignore it if you like. When we increase something by 1/4, we are multiplying it by 1 + 1/4 = 5/4, so the answer here must be (1/2)*(5/4) = 5/8 = 62.50 %.
Answer : A
Answer: (A) 62.50%
Question: Four milkmen rented a pasture. A grazed 24 cows for 3 months, B 10 cows for 5 months, C 35 cows for 4 months and D 21 cows for 3 months. If A’s share of rent is Rs.720, find the total rent of the field.
(A) Rs.3250
(B) Rs.3350
(C) Rs.3450
(D) Rs.3550
(E) Rs.3650
Rationale: Ratio of shares of A, B, C, D = (24 * 3) : (10 * 5) : (35 * 4) : (21 * 3)
= 72 : 50 : 140 : 63
Let total rent be Rs.x. Then, A’s share = Rs. 72x/325.
Therefore, 72x/325 = 720 => x = 720 * 325/72 = 3250.
Hence, total rent of the field is Rs.3250.
ANSWER:A
Answer: (A) Rs.3250
Question: Sandy purchased 20 dozen toys at the rate of $144 per dozen. Sandy sold each toy at the rate of $15. What was the percentage profit?
(A) 15%
(B) 25%
(C) 35%
(D) 45%
(E) 55%
Rationale: A dozen toys cost $144, so each toy cost $12.
selling price / cost price = 15 / 12 = 1.25
The percentage profit is 25%.
The answer is B.
Answer: (B) 25%
Question: The total number of digits used in numbering the pages of a book having 366 pages is
(A) 732
(B) 990
(C) 1098
(D) 1305
(E) 1605
Rationale: Explanation:
Total number of digits
= (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)
= (1 x 9 + 2 x 90 + 3 x 267) = (9 + 180 + 801) = 990.
Answer: B
Answer: (B) 990
Question: If x is odd and y is odd, then x + y is
(A) Odd
(B) Odd whenever xy is even
(C) Even whenever xy is odd
(D) Even
(E) It cannot be determined
Rationale: x is odd and y is odd, then x + y is
Let's take x=9 and y=5.
x+y=9+5=14.
x+y=14=even.
Option: D
Answer: (D) Even
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
(A) 2/27
(B) 2/29
(C) 2/21
(D) 2/22
(E) 2/27
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer:C
Answer: (C) 2/21
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 55 hrs and a machine of type S does the same job in 22 hours. If the company used the same number of each type of machine to do the job in 5 hours, how many machines of type R were used?
(A) 22/7
(B) 28/7
(C) 23/7
(D) 25/7
(E) 22/7
Rationale: Rate of machine R =1/55
Rate of machine S =1/22
since same no of machines used for R and S to do the same work in 5 hrs
So collective rate needed to finish the work in 5 hrs= 1/5
Let the no of machine be x
So, x/55 +x/22 =1/5
7x=22
x=22/7
So no of machine R is 22/7
Answer E
Answer: (E) 22/7
Question: A highway is to be divided into four lanes. For this purpose, three yellow stripes are painted so that stripes divide the highway into four lanes. If 3 gallons of paint cover an area of 5P square feet of highway, how many gallons of paint are needed to paint two stripes x inches wide on a stretch of highway m miles long? (1 mile = 5280 feet and 1 feet = 12 inches)
(A) 792mx/P
(B) 264mx/P
(C) 792P/mx
(D) 264P/mx
(E) 880mx/P
Rationale: 1 square foot needs 3/5P gallons of paint.
The width of each stripe is x/12 feet.
The length of each stripe is 5280m feet.
The area of each stripe is (5280m)(x/12) = 440mx square feet.
For three stripes, the total area is 1320mx square feet.
The number of gallons needed is (1320mx)*(3/5P) = 792mx/P gallons.
The answer is A.
Answer: (A) 792mx/P
Question: In how many years, Rs. 75 will produce the same interest at 6% as Rs. 800 produce in 2 years at 4½% ?
(A) 4 years
(B) 16 years
(C) 8 years
(D) 9 years
(E) 12 years
Rationale: Explanation :
Let Simple Interest for Rs.75 at 6% for n years = Simple Interest for Rs.800 at 4½ % for 2 years
75×6×n/100=800×9/2×2/100
75×6×n=800×9/2×2
75×6×n=800×9
n=16 years
Answer : Option B
Answer: (B) 16 years
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is ?
(A) 1/38
(B) 1/36
(C) 1/39
(D) 1/31
(E) 1/29
Rationale: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216 = 1/36
Answer:B
Answer: (B) 1/36
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is ?
(A) 1/6
(B) 1/2
(C) 1/9
(D) 1/1
(E) 1/5
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2
= 1/2.
Answer: B
Answer: (B) 1/2
Question: If S is a positive integer, which of the following must be odd?
(A) S+1
(B) S^2+S
(C) S^2+S+1
(D) x^2−1
(E) 3x^2−3
Rationale: A. S+1 = can be odd or even. Since O + O =E or E + O = O
B. S^2 + S = S(S+1). Since from the above derivation we already know the term S+1 can be Odd or Even, directly substitute here. S(ODD) = Even (When S is Even) or S(EVEN) = EVEN [When S is ODD]
C. Here's the answer. Since we know the term S^2 + S can always take a EVEN number, EVEN + 1 = ODD
Hence C.
Answer: (C) S^2+S+1
Question: Present birth rate is 32 per thousand while death rate is 11 per thousand. What will be the percentage increase in the rate of population?
(A) 0.21%
(B) 21%
(C) 0.021%
(D) 2.1%
(E) None of these
Rationale: birth rate=32/1000=0.032
death rate=11/1000=0.011
increase in population=0.032-0.011=0.021=2.1%
ANSWER:D
Answer: (D) 2.1%
Question: What will be the output of the following code statements?
Integer a = 13, b = 39, c = 10 print (a × b / c) – c
(A) 65
(B) 26
(C) 29
(D) 26
(E) 41
Rationale: Explanation:
Apply BODMAS rule
13 × 39 = 507/10-10 =50.7 –10 =40.7
Answer:E
Answer: (E) 41
Question: The instructions state that Cheryl needs 2/9 square yards of one type of material and 1/8 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 4/18 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?
(A) 1/12
(B) 1/9
(C) 1/8
(D) 1 1/9
(E) 2 1/9
Rationale: Total bought = 2/9+1/8
left part 4/18--->2/9
so used part 2/9+1/8-2/9=1/8
ANSWER:C
Answer: (C) 1/8
Question: The concentration of spirit in three different vessels A, B and C are 30%, 30% and 25% respectively. If 4 litres from vessel A, 5 litres from vessel B and 6 litres from vessel C are mixed, find the concentration of spirit in the resultant solution.
(A) 32%
(B) 33%
(C) 34%
(D) 35%
(E) 28%
Rationale: Quantity of spirit in new solution=(4*30/100)+(5*30/100)+(6*25/100)=1.2+1.5+1.5=4.2 liters
So % concentration of spirit=100*4.2/(4+5+6)=28%
ANSWER:E
Answer: (E) 28%
Question: Arnold wanted to create a perfect shade of pink for his new canvas painting. He started out replacing 25% of a 100% red colored paint with white. He then further replaced 15% of this shade with white. Finally, he repeated the process by replacing 10% of the shade with white. What was the final percentage of red in Arnold's pink paint?
(A) 62.40%
(B) 51%
(C) 68.21%
(D) 57.37%
(E) 70%
Rationale: Quick answer: 100x0.75x0.85x0.9
We begin with 100% red paint. 25% of this is replaced with white paint which leaves us with a mixture of 75% red paint (as 25% is white)
Next, 15% of this mixture is further mixed with white paint. That implies that 85% of the previous red paint remains. Hence, the new percentage is 75x0.85% = 63.75%
Finally, 10% of the new paint mixture is again mixed with white. This leaves us with 90% of the previous red quantity. So the final percentage of red is 63.75x0.9% = 57.37%
Answer: D
Answer: (D) 57.37%
Question: If an item costs Rs.3 in '99 and Rs.203 in '00.What is the % increase in price?
(A) 200/3 %
(B) 200/6 %
(C) 100%
(D) 200%
(E) none of these
Rationale: increase is 203-3=200
%increase is 200*100/3=6666.667%
ANSWER:E
Answer: (E) none of these
Question: In a certain random experiment, exactly one of the outcomes A, B, and M will occur. In each random experiment, the probability that outcome A will occur is 1/3 , and the probability that outcome B will occur is 1/3. What is the probability that when the random experiment is conducted 6 independent times, each of outcomes A, B, and M will occur twice?
(A) 5/243
(B) 1/12
(C) 10/81
(D) 1/6
(E) 16/81
Rationale: Number of ways in which a group of 2A,2B,2M can be formed in any order = 6!/(2!*2!*2!) [ formula for total of 6 items with 2 each of similar kind)
Total number of ways in which the die can be thrown independently = _ _ _ _ _ _ ; there are 6 places .First can be filled in 3 different ways A/B/M; Second in 3 diff ways again and so on.
So total number of ways = 3X3X3X3X3X3 = 3^6
There fore probability = 6!/(2!x2!x2!) by 3^6 = 90/3^6 = 10/81 Answer C
Answer: (C) 10/81
Question: A man buys a cycle for Rs. 1600 and sells it at a loss of 15%. What is the selling price of the cycle?
(A) s. 1090
(B) s. 1360
(C) s. 1190
(D) s. 1202
(E) s. 1256
Rationale: S.P. = 85% of Rs. 1600 = Rs.85/100x 1600	= Rs. 1360
ANSWER :B
Answer: (B) s. 1360
Question: Which of the following data sets has the largest standard deviation?
(A)  {1, 2, 3, 4, 5}
(B)  {2, 3, 3, 3, 4}
(C)  {2, 2, 2, 4, 5}
(D)  {0, 2, 3, 4, 6}
(E)  {-1, 1, 3, 5, 7}
Rationale: since we are asked to compare 'standard deviation', we should look out for similarity between all the sets..
The SIMILARITY is - the SUM of all sets is equal =15..
and hence average = 15/5 = 3...
Now we have 5 different sets which have AVG as 3, so we will look for the spread of the other elements of set around the AVERAGE..
clearly E has a range of 7-(-1) or 8, and has the highest standard deviation..
ans E
Answer: (E)  {-1, 1, 3, 5, 7}
Question: At present, the ratio between the ages of Arun and Deepak is 5:4. After 5 years, Arun's age will be 40 years. What is the age of Deepak at present?
(A) 28
(B) 26
(C) 24
(D) 22
(E) 20
Rationale: Let the present ages of Arun and Deepak be 5x and 4x years respectively.
Then, 5x + 5 = 40 => x = 7
Deepak's age = 4x = 28 years.
Answer: A
Answer: (A) 28
Question: Twenty four men can do a work in 35 days. How many men are required to complete the work in 21 days?
(A) 11
(B) 40
(C) 99
(D) 77
(E) 21
Rationale: We have M1 D1 = M2 D2
So, 24 * 35 = M2 * 21 => M2
= 40.
Answer: B
Answer: (B) 40
Question: An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point?
(A) 5 hrs 21 min
(B) 4 hrs 21 min
(C) 6 hrs 41 min
(D) 6 hrs 21 min
(E) 4 hrs 34 min
Rationale: D
6 hrs 21 min
Time taken to cover 600 km = 600/100 = 6 hrs.
Number of stoppages = 600/75 - 1 = 7
Total time of stoppages = 3 * 7 = 21 min
Hence, total time taken = 6 hrs 21 min.
Answer: (D) 6 hrs 21 min
Question: In a kilometer race, A beats B by 20 meters or 10 seconds. What time does A take to complete the race?
(A) 490 sec
(B) 190 sec
(C) 176 sec
(D) 716 sec
(E) 123 sec
Rationale: Time taken by B run 1000 meters
= (1000 * 10)/20 = 500 sec.
Time taken by A = 500 - 10
= 490 sec.
Answer:A
Answer: (A) 490 sec
Question: A group of 4 students bought movie tickets in one row next to each other. If Bob and Lisa are in this group, what is the probability that Bob and Lisa will each sit next to only one of the three other students from the group?
(A) 5.55%
(B) 16.67%
(C) 15.75%
(D) 20.45%
(E) 25%
Rationale: The question basically asks about the probability that Bob and Lisa sit at the ends.
The total # of sitting arrangements is 4!.
Desired arrangement is either BYZL or LYZB. Now, YZ can be arranged in 2! ways, therefore total # of favorable arrangements is 2*2!.
P=(favorable)/(total)=(2*2!)/4!=1/6.
Answer: B.
Answer: (B) 16.67%
Question: AB
+BA
___
141
In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B?
(A) 6
(B) 8
(C) 9
(D) 11
(E) 12
Rationale: two ways to do it..
1) straight logic..
we can see that ones digit is 1 when units digit B and A are added..
only 12 fits in..
E
Answer: (E) 12
Question: If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is:
(A) 20:15:16
(B) 20:15:11
(C) 20:15:12
(D) 20:15:18
(E) 20:19:19
Rationale: 6A = 8B = 10 C
A:B:C = 1/6:1/8:1/10
= 20:15:12
Answer:C
Answer: (C) 20:15:12
Question: Find the invalid no.from the following series 3, 7, 15, 27, 63, 127, 255
(A) 3
(B) 7
(C) 27
(D) 63
(E) 127
Rationale: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 27 is wrong.
C
Answer: (C) 27
Question: (1.00001)(0.99999) - (1.00006)(0.99994) =
(A) 35(10^-10)
(B) 10^-10
(C) 3(10^-10)
(D) 10^-5
(E) 3(10^-5)
Rationale: (1.00001*0.99999)-(1.00006*0.99994)
= (1+0.00001)(1-0.00001) - (1+0.00006)(1-0.00006)
= 1 - (0.00001)^2 - 1 + (0.00006)^2
= -(0.0000000001) + (0.0000000036)
= 0.0000000035=35(10^-10)
Answer A
Answer: (A) 35(10^-10)
Question: Find ? x 11 = 555555
(A) 505
(B) 5050
(C) 50505
(D) 5005
(E) None of these
Rationale: Answer
Let N x 11 = 555555
Then N = 555555 / 11 = 50505.
Correct Option: C
Answer: (C) 50505
Question: In 1982 and 1983, Company B’s operating expenses were $12.0 million and $13.0 million, respectively, and its revenues were $15.6 million and $18.8 million, respectively. What was the percent increase in Company B’s profit (revenues minus operating expenses) from 1982 to 1983 ?
(A) 3%
(B) 61 1/9%
(C) 25%
(D) 33 1/3%
(E) 60%
Rationale: Profit in 1982 = 15.6 - 12 = 3.6 million $
Profit in 1983 = 18.8 - 13 = 5.8 million $
Percentage increase in profit = (5.8-3.6)/3.6 * 100 %
= 61 1/9 %
Answer B
Answer: (B) 61 1/9%
Question: Avg cost of 3 sharpners and 6 erasers is Rs.72. The avg cost of 6 sharpners and 8 erasers is Rs.112. Find the total cost of 20 sharpners and 20 erasers?
(A) 190
(B) 160
(C) 130
(D) 200
(E) 180
Rationale: Avg cost of 3 sharpners and 6 erasers is Rs.72
(3 sharpner + 6 erasers) 9=72
therefore 1 sharpner cost is 72/9=8, so 3 sharpner cost is 3x8=24 and 6 erasers cost is 6x8=48
Again, avg cost of 6 sharpners and 8 erasers is Rs.112
(6 sharpner + 8 erasers) 14=112
therefore 1 sharpner cost is 112/14=8, so 6 sharpner cost is 6x8=48 and 8 erasers cost is 8x8=64
So 20 sharpner cost is (20/a)=160 and 20 erasers cost is (20x8)=160
ANSWER:B
Answer: (B) 160
Question: Sachin is younger than Rahul by 4 years. If their ages are in the respective ratio of 7:9, how old is Sachin?
(A) 24.9
(B) 24.6
(C) 24.2
(D) 24.8
(E) 24.5
Rationale: Let Rahul's age be x years.
Then, Sachin's age = (x - 7) years.
(x - 7)/x = 7/9
2x = 63 => x = 31.5
Hence, Sachin's age = (x - 7) = 24.5 years.
Answer: E
Answer: (E) 24.5
Question: A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
(A) 9:1
(B) 8:1
(C) 9:8
(D) 2:1
(E) 1:1
Rationale: Milk = 3/5 * 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
Amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.
The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1.
Answer:A
Answer: (A) 9:1
Question: Simplify
80âˆ’[5âˆ’(6+2(7âˆ’8âˆ’5Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯))]
(A) 23
(B) 25
(C) 89
(D) 30
(E) 32
Rationale: Explanation:
=80âˆ’[5âˆ’(6+2(7âˆ’8+5))]
(Please check due to overline, sign has been changed)
=80âˆ’[5âˆ’(6+2Ã—4))]
=80âˆ’[âˆ’9]=80+9=89
Option C
Answer: (C) 89
Question: In a game of 90 points, A can give B 5 points and C 15 points. then how many points B can give C in a game of 60?
(A) 2.82
(B) 7.82
(C) 5.82
(D) 12.82
(E) 8.82
Rationale: In a game of 90 points,A give B 5 points and c 25 points means B=85,C=65
In 85 points B give 15 since 80-65=15
In 50 points B gives=50*15/85=8.82
ANSWER:E
Answer: (E) 8.82
Question: ABCD is a square where AB =âˆš6016. Let X be a point on AB and Y be a point on CD such
that AX = CY . Compute the area of trapezoid AXYD.
(A) 3008
(B) 2002
(C) 1008
(D) 2016
(E) 3000
Rationale: Note that trapezoids AXY D and BXY C are congruent, so the area of AXY D is
always
6016/2= 3008 .
correct answer A
Answer: (A) 3008
Question: 12 is what % of 80?
(A) 6
(B) 6.67
(C) 12
(D) 13
(E) 15
Rationale: We assume that 80 is 100%
assume 'x' is value we looking for
here,
80 = 100% and
x% = 12
therefore,
100/x = 80/12
100/x = 6.6667
x = 15
E
Answer: (E) 15
Question: 33
a3
+4b
___
88
If a and b represent positive single digits in the correctly worked computation above, what is the value of the two digit integer ab?
(A) 12
(B) 10
(C) 13
(D) 24
(E) 34
Rationale: 3+3+b=8
b=2
3+a+4=8
a=1
ab=12
ans=A
Answer: (A) 12
Question: A train running at 1/4 of its own speed reached a place in 12 hours. How much time could be saved if the train would have run at its own speed?
(A) 9 hrs
(B) 10hrs
(C) 12hrs
(D) 15hrs
(E) 6hrs
Rationale: time taken if run its own speed = 1/4*12 = 3 hrs
Time saved = 12 - 3 = 9 hrs
Answer : A
Answer: (A) 9 hrs
Question: A collector collects stamps from foreign countries. In June, she gave 20 percent of her stamps to her friend. In July, she gave 35 percent of her remaining stamps to another friend. If these were the only changes in the number of stamps in the stamp collection during those two months, what percent of her collection at the beginning of June did she give to away in June and July?
(A) 32%
(B) 36%
(C) 40%
(D) 44%
(E) 48%
Rationale: Let x be the number of stamps in the original collection.
The percentage of the collection given away is:
0.2x + 0.35(0.8x) = 0.2x + 0.28x = 0.48x = 48%
The answer is E.
Answer: (E) 48%
Question: How much pure alcohol should be added to 400ml of a 15% solution to make the strength of solution 32%?
(A) 100 ml
(B) 60 ml
(C) 120 ml
(D) 130 ml
(E) 150 ml
Rationale: 400ml has 15% alcohol i.e 60ml . This means we have 340ml of water or the liquid with which alcohol is mixed
Let V be the volume of alcohol added to make the strength 32%
then V/340+V = 32/100. solving this we get V as 160ml
so we need to add 160 -60 = 100 ml of alcohol
ANSWER:A
Answer: (A) 100 ml
Question: The tailor has a 10 meter long piece of fabric for which to sew a ball room dress.
She has to cuts this fabric into strips of 200 centimeters each.
How long will it take the tailor to complete this tasks if each 200 centimeter took 5 minutes to cut ?
(A) 150
(B) 200
(C) 188
(D) 245
(E) 123
Rationale: The tailors would need to cut the fabric 49 times thus the total amount spent would be 245 minutes. The answer is D
Answer: (D) 245
Question: Find the largest number of four digits which is exactly divisible by 26,18,12,15
(A) 9700
(B) 9710
(C) 9360
(D) 9130
(E) 9140
Rationale: Explanation:
LCM of 26-18-12-15 is 2340.
After dividing 9999 by 2340 we get 639 remainder.
So answer will be 9999-639 = 9360
Option C
Answer: (C) 9360
Question: Set R has a mean of 15 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?
(A) {11,26}
(B) {18,19}
(C) {16,18}
(D) {16,16}
(E) {14,16}
Rationale: The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 15,the values (14,16) are closer than others.
Hence Answer : E
Answer: (E) {14,16}
Question: Eggs are sold in packages of six or eleven only. If Doris bought 78 eggs exactly, what could be the number of large packs Doris bought?
(A) 6.
(B) 2.
(C) 3.
(D) 5.
(E) 4.
Rationale: No strategy involved. Simple question demanding fast calculation.
11x6 = 66=> 78-66=12 => 12/6 is an integer
Ans A. 6.
Good luck
Answer: (A) 6.
Question: There 3 kinds of books in the library physics, chemistry and biology. Ratio of physics to chemistry is 3 to 2; ratio of chemistry to biology is 4 to 3, and the total of the books is more than 3000. Which one of following can be the total W of the book?
(A) 3003
(B) 3027
(C) 3024
(D) 3021
(E) 3018
Rationale: First, you have to find the common ratio for all 3 books. You have:
P:C:B
3:2 --> multiply by 2 (gives you row 3)
4:6
6:4:3
Hence:
P:C:B:T(Total)W
6:4:3:13 ----> This means, the Total Number must be a multiple of 13.
Answer A is correct since 299 is divisible by 13, hence is 2990 and so is 3003 (2990+13).
Answer: (A) 3003
Question: The sum of squares of two numbers is 80 and the square of their difference is 36. The product of the two numbers is.
(A) 22
(B) 44
(C) 58
(D) 116
(E) None
Rationale: Explanation :
Let the numbers be x and y . Then
x2+y2=80 and (x−y)2=36
(x−y)2=36⇒x2+y2−2xy=36
⇒2xy=(x2+y2)−36=80−36=44
⇒xy=22
Correct Option: A
Answer: (A) 22
Question: A salesperson receives a base salary of $900 per month and a commission of 7.5% of the selling price of each item sold above the first 50 item. If this month she sold 210 items for $150 each, what will her monthly salary be?
(A) $1,500
(B) $1,800
(C) $2,100
(D) $2,700
(E) $2,800
Rationale: Ans : 900+ 7.5 % * 150 * (210-50) = $ 2700
Answer D
Answer: (D) $2,700