mathewhe/aqua_rat huggingface dataset:
Question: The incomes of two persons A and B are in the ratio 3:4. If each saves Rs.100 per month, the ratio of their expenditures is 1:2 . Find their incomes?
(A) 827,988
(B) 146,788
(C) 150,200
(D) 154,863
(E) 154,983
Rationale: The incomes of A and B be 3P and 4P.
Expenditures = Income - Savings
(3P - 100) and (4P - 100)
The ratio of their expenditure = 1:2
(3P - 100):(4P - 100) = 1:2
2P = 100 => P = 50
Their incomes = 150, 200
Answer:C
Answer: (C) 150,200
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 48 years now, the son's age five years back was:
(A) 14
(B) 17
(C) 19
(D) 22
(E) 24
Rationale: Let the son's present age be x years. Then, (48 - x) = x
2x = 48.
x = 24.
Son's age 5 years back (24 - 5) = 19 years.
answer :C
Answer: (C) 19
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 111.12 m
(B) 119.12 m
(C) 111.13 m
(D) 121.12 m
(E) 111.52 m
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
Answer:A
Answer: (A) 111.12 m
Question: If x is equal to the sum of the even integers from 40 to 60 inclusive, and y is the number of even integers from 40 to 60 inclusive, what is the value of x+y?
(A) 550
(B) 551
(C) 560
(D) x+y=561
(E) 572
Rationale: sum of even integers = even number ( x is even)
number of even integers =11 ( y is odd )
so x+y = odd
A, C, E out ( all even)
Left with B and D :551, 561
If you have ever added even numbers you see that the pattern is 0,2,4,6,8 and 2+4+6+8 =20
{ there are 11 integers 5 in the 40's , 5 in the 50's and 60 , so when u add the u get 200+250+20+20+60 = 550}
hence the sum is 550 ( x=550) or x+y cannot be 551 since x =550
hence answer is D
Answer: (D) x+y=561
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 2:3:5. If there are in all Rs.40.50, the number of 50 paisa coins is?
(A) 18
(B) 16
(C) 12
(D) 24
(E) 36
Rationale: 2x 3x 5x
50 25 100
100x + 75x + 500x = 4050
675x = 4050
x = 6 => 2x = 12
Answer: C
Answer: (C) 12
Question: If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 105 games will be played during the tournament. Find the number of participants.
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: Let P be the number of participants.
PC2 = 105
(P)(P-1) = 210 = 15*14
P = 15
The answer is A.
Answer: (A) 15
Question: A train running at the speed of 60 km/hr crosses a pole in 12 sec. What is the length of the train?
(A) 287
(B) 699
(C) 677
(D) 168
(E) 200
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 12 = 200 m
Answer: E
Answer: (E) 200
Question: Given that 268x74= 19632, find the value of 2.68x.74.
(A) 1.9632
(B) 1.0025
(C) 1.5693
(D) 1.0266
(E) None
Rationale: Solution
Sum of decimals places	=(2+2)
= 4.
Therefore,	= 2.68×.74
= 1.9632
Answer A
Answer: (A) 1.9632
Question: Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?
(A) 70% p.a
(B) 50% p.a
(C) 20% p.a
(D) 10% p.a
(E) 90% p.a
Rationale: Explanation:
Rs.1440 - 1200 = Rs.240 is the interest on Rs.1200 for one year.
Rate of interest = (100 * 240) / (100 * 1) = 20% p.a
Answer: C
Answer: (C) 20% p.a
Question: John has $1,200 at the beginning of his trip, after spending money, he still has exactly $800 less than he spent on the trip. How much money does John still have?
(A) $200
(B) $400
(C) $600
(D) $800
(E) $1,200
Rationale: Suppose total money spent = x
Not spend (Money he still has)= x-800
x+x-800 = 1200
x= 1000
Money not spend= 1000-800= 200
Answer : A
Answer: (A) $200
Question: From among the 39 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
(A) 1360
(B) 1260
(C) 1060
(D) 1482
(E) 1460
Rationale: There are 39 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 39 ways. When one person is appointed as leader, we are left with 35 students. Out of these 38 teachers, we can select one class representative. So, a class representative can be selected in 38 ways. Hence, the number of ways in which a leader and class representative can be selected = 39 x 38 = 1482
ANSWER:D
Answer: (D) 1482
Question: What will be the fraction of 33.33%
(A) 1/4
(B) 1/5
(C) 1/3
(D) 1/8
(E) None of above
Rationale: Explanation:
It will 33.33*1/100 = 1/3
Answer: Option C
Answer: (C) 1/3
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 258 m
(B) 240 m
(C) 278 m
(D) 289 m
(E) 268 m
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer:B
Answer: (B) 240 m
Question: An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 4 o’clock in the afternoon?
(A) 60°
(B) 90°
(C) 180°
(D) 320°
(E) 240°
Rationale: Sol.
Angle traced by the hour hand in 8 hours = [360/12 * 8]° = 240°
Answer E
Answer: (E) 240°
Question: 10 litres of water are poured into an aquarium of dimensions 50cm length, 10cm breadth, and 40cm height. How high (in cm) will the water rise?
(1 litre = 1000cm³)
(A) 6
(B) 8
(C) 10
(D) 20
(E) 40
Rationale: lXbXh= 10000
h= 10000/50*10= 20 cm
'D' is the answer.
Answer: (D) 20
Question: Anna and Carol buy CDs and tapes at a music store that sells each of its CDs for a certain price and each of its tapes for a certain price. Anna spends twice as much as Carol spends, buying three times as many CDs and the same number of tapes. If Carol spends $40.00 on four CDs and five tapes, how much does one tape cost?
(A) $4.00
(B) $6.25
(C) $12.00
(D) $25.00
(E) $100.00
Rationale: CD => C
Type => T
Carol: 4C+5T=40
Anna: 12C+5T=80
12C-4C=40
8C=40
C=5
4C+5T=40
20+5T=40
5T=20
T=4
Answer is A
Answer: (A) $4.00
Question: A lends Rs. 2500 to B and a certain to C at the same time at 7% p.a. simple interest. If after 4 years, A altogether receives Rs. 1120 as interest from B and C, then the sum lent to C is?
(A) 1522
(B) 1500
(C) 1789
(D) 2689
(E) 2689
Rationale: Let the sum lent to C be Rs. x. Then,
(2500 * 7 * 4) / 100 + (x * 7 * 4) / 100 = 1120
7/25 x = (1120 - 700) => x = 1500
Answer: B
Answer: (B) 1500
Question: Ages of two persons differ by 18 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age
(A) 12,28
(B) 15,33
(C) 16,32
(D) 18,34
(E) 19,34
Rationale: Explanation:
Let the age of younger person is x,
Then elder person age is (x+18)
=> 3(x-6) = (x+18-6) [6 years before]
=> 3x-18 = x+12
=> x = 15.
So other person age is x + 18 = 33
Answer: Option B
Answer: (B) 15,33
Question: There are 100 men in town. Out of which 85% were married, 70% have a phone, 75% own a car, 80% own a house. What is the maximum number of people who are married, own a phone, own a car and own a house?
(A) 20
(B) 15
(C) 10
(D) 5
(E) None of these
Rationale: % of married = 85%
% of phone = 70%
% of car = 75%
% of house = 80.
Therefore,
% of not married = 15%
% of not having phone = 30%
% of not owning car = 25%
% of not having house = 20%
So, % of not having any of these things = 15 +25+ 30 + 20 = 90%
So, % of people having all = 100 -90 = 10%
Thus, people = 10.
ANSWER -OPTION C
Answer: (C) 10
Question: To 15 lts of water containing 20% alcohol, we add 5 lts of pure water. What is % alcohol.
(A) 25%
(B) 35%
(C) 15%
(D) 18%
(E) 19%
Rationale: since 20% alcohol in 15 lit=(15*20)/100=3 lit
since total water=(15-3)+5=17
total mix=3+17=20
% of alcohol=(3/20)*100=15%
ANSWER:C
Answer: (C) 15%
Question: A student got 71% in math and 81% in history. To get an overall average of 75%, how much should the student get in the third subject?
(A) 63%
(B) 75%
(C) 77%
(D) 79%
(E) 81%
Rationale: 71 + 81 + x = 3*75
x = 73
The answer is A.
Answer: (A) 63%
Question: A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 12% while buying and by 30% while selling. What is his percentage profit?
(A) 10.22%
(B) 20.22%
(C) 21.22%
(D) 60%
(E) Can't be calculated
Rationale: The owner buys 100 kg but actually gets 112kg;
The owner sells 100 kg but actually gives 70kg;
Profit: (112-70)/70*100=~60%
Answer: D.
Answer: (D) 60%
Question: In a class of 35 students 26 play football and play 20 long tennis, if 17 play above, many play neither?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: 26 + 20 - 17 = 29
35 - 29 = 6 play neither
Answer is A
Answer: (A) 6
Question: A and B are two circles. The radius of A is thrice as large as the diameter of B. What is the ratio between the areas of the circles?
(A) 1:18.
(B) 1:20.
(C) 1:4.
(D) 1:36.
(E) 1:16.
Rationale: Given : The radius of A is thrice as large as the diameter of B. => R(a) = 3*D(b) = 3*2*R(b) = 6R(b). The radius are in ratio of 1:6 thus the area will be in the ratio of square of radius. 1:36. Hence D.
Answer: (D) 1:36.
Question: The sum of 3 hours 45 minutes and 4 hours 55 minutes is approximately what percent of a day?
(A) 33%
(B) 34%
(C) 35%
(D) 36%
(E) 37%
Rationale: Since the question is asking for an approximate percentage
3:45+4:55 ~ 9 hours
% of day = 9*100/24 ~ 9*100/25= 36%
Answer is D.
Answer: (D) 36%
Question: If it is 6:17 in the evening on a certain day, what time in the morning was it exactly 2,880,717 minutes earlier? (Assume standard time in one location.)
(A) 6:22
(B) 6:24
(C) 6:27
(D) 6:20
(E) 6:32
Rationale: 6:17minus 2,880,717in any way must end with 0, the only answer choice which ends with 0 is D.
Answer: D.
Answer: (D) 6:20
Question: There are 7 meetings A,B,C,D,E,F,G. One meeting should be happen in one day. Meeting A is on Sunday and the meetings shoud be happen afterB. Then E ,F,G meeting occur in 3 conjucutive day. And meeting G is on Saturday.Next metting should occur in which day?
(A) sunday
(B) monday
(C) tuesday
(D) wednesday
(E) friday
Rationale: It is given that E, F, G meetings occur in 3 consecutive days and meeting G is on Saturday. It is also given that A is on Sunday so definitely days for E and F would be Friday and Thursday. Since meetings should be happen after B so the day for B would be Wednesday so next meeting should occur in monday
ANSWER:B
Answer: (B) monday
Question: Three numbers are in the ratio 1:2:3 and their H.C.F is 12. The numbers are:
(A) 4, 8, 12
(B) 5, 10, 15
(C) 10, 20, 30
(D) 12, 24, 36
(E) 12, 24, 39
Rationale: Let the required numbers be x, 2x and 3x. Then, their H.C.F = x. So, x = 12.
The numbers are 12, 24, 36.
ANSWER:D
Answer: (D) 12, 24, 36
Question: The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:
(A) 2.3 m
(B) 4.6 m
(C) 7.8 m
(D) 9.2 m
(E) 10.1
Rationale: Let AB be the wall and BC be the ladder.
Then, ACB = 60º and AC = 4.6 m.
AC/BC= cos 60º =1/2
BC = 2 x AC
= (2 x 4.6) m
= 9.2 m.
Answer: Option D
Answer: (D) 9.2 m
Question: The combined area of the two black squares is equal to 1000 square units. A side of the larger black square is 8 units longer than a side of the smaller black square. What is the combined area of the two white rectangles in square units?
(A) 928
(B) 936
(C) 948
(D) 968
(E) 972
Rationale: The length of a smaller square - x;
The length of a larger square - x+8;
The area of entire square - x^2+(x+8)^2=1000 --> 2x^2+16x=936;
The combined area of the two white rectangles - x(x+8)+x(x+8)=2x^2+16x --> look up: 2x^2+16x=936.
Answer: B.
Answer: (B) 936
Question: If 8 gallons of gasoline are added to a tank that is already filled to 3/4 of its capacity, the tank is then filled to 9/10 of its capacity. How many gallons does the tank hold?
(A)  20
(B)  24
(C)  36
(D)  48
(E)  60
Rationale: Let the Capacity of the tank=C
(3/4)C + 8 = (9/10)C
=>(9/10)C - (3/4)C = 8
=>(3/20)C = 8
=>C = (8*20)/3 = 53.33
Number of gallons of gasoline that the tank currently holds = 3/4*C +8 = 39.99+8 = 47.99=48
Answer D
Answer: (D)  48
Question: If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, what is the probability that xy will be even?
(A) 1/6
(B) 1/3
(C) 1/2
(D) 2 by 3
(E) 5/6
Rationale: In order to make even nos. by multiplication,
we should have even * odd, odd * even or even * even
Total even nos. possible by multiplying nos. from the 2 sets:
(1*6);
2* any of the three from Set B;
3*6;&
4* any of the three from set B
1+3+1+3=8
Total possibilities=4 * 3=12
P(event)=8/12 or 2/3
Ans D
Answer: (D) 2 by 3
Question: In how many different ways can the letters of the word â€˜CASESâ€™ be arranged?
(A) 250
(B) 280
(C) 60
(D) 310
(E) 360
Rationale: Number of ways = 5!/2! = 5X4X3X2X1/2X1 = 60
C
Answer: (C) 60
Question: 100kg of an alloy A is mixed with 200 kg of alloy B. If alloy A has lead and tin in the ratio 5:3 and alloy B has tin and copper in the ratio 2:3, then the amount of tin in the new alloy is?
(A) 100.6kg
(B) 120.3kg
(C) 117.5kg
(D) 110.8kg
(E) 114kg
Rationale: Quantity of tin in 100kg of A = 100*3/8 = 37.5kg
Quantity of tin in 200kg of B = 200*2/5 = 80kg
Quantity of tin in the new alloy = 37.5+80 = 117.5kg
Answer is C
Answer: (C) 117.5kg
Question: a and b are positive integers less than or equal to 9 and multiple of 4. If a and b are assembled into the seven-digit number abaabab, which of the following must be a factor of abaabab?
(A) 3
(B) 4
(C) 5
(D) 7
(E) 8
Rationale: The last two digit of the number are ab. Both a and b are multiple of 4,thus the last two digits are divisible by 4, which makes the number abaabab divisible by 4. Thus 4 is always a factor of abaabab.
Answer: B
Answer: (B) 4
Question: A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?
(A) 126
(B) 776
(C) 266
(D) 299
(E) 271
Rationale: Explanation:
There are 8 students and the maximum capacity of the cars together is 9.
We may divide the 8 students as follows
Case I: 5 students in the first car and 3 in the second
Or Case II: 4 students in the first car and 4 in the second
Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.
Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.
Therefore, the total number of ways in which 8 students can travel is:
\inline {\color{Blue}8C_{3}+8C_{4}}=56 + 70= 126
Answer: A) 126
Answer: (A) 126
Question: Susan drove an average speed of 15 miles per hour for the first 40 miles of a tripthen at a average speed of 60 miles/hr for the remaining 20 miles of the trip if she made no stops during the trip what was susan's avg speed in miles/hr for the entire trip
(A) 35
(B) 20
(C) 45
(D) 50
(E) 55
Rationale: Avg. speed = total distance / total time
Total distance = 60 miles
Total time = 40 / 15 + 20/60 = 3
Avg. speed = 20.
Answer - B
Answer: (B) 20
Question: A man is 35 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
(A) 78 years
(B) 22 years
(C) 33 years
(D) 66 years
(E) 65 years
Rationale: Let's Son age is x, then Father age is x+35.
=> 2(x+2) = (x+35+2)
=> 2x+4 = x+37
=> x = 33 years
Answer: C
Answer: (C) 33 years
Question: A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent T of the cost would the gross profit on the item have been if it had been sold without the discount?
(A) 20%
(B) 40%
(C) 50%
(D) 60%
(E) 75%
Rationale: Let the Market Price of the product is MP.
Let the Original Cost Price of the product is CP.
Selling Price (Discounted Price) = 100%of MP - 20%MP
= 80% of MP. ---------------- (1)
Profit made by selling at discounted price = 20% of CP -------------- (2)
Apply the formula:
Profit T= Selling Price - Original Cost Price
=> 20% of CP = 80% of MP - 100% CP
=> MP = 120CP/80 = 3/2 (CP)
Now if Product is sold without any discount, then,
Profit = Selling Price (without discount) - Original Cost Price
= Market Price - Original Cost Price
= MP - CP
= 3/2 CP - CP
= 1/2 CP
=50%of CP
Thus, Answer should beC.
Answer: (C) 50%
Question: If x is 11 percent greater than 80, then x =
(A) 88.8
(B) 91.0
(C) 88.0
(D) 70.9
(E) 71.2
Rationale: 11% of 80 = (80*0.11) = 8.8
11% greater than 80 = 80 + 8.8 = 88.8
Answer is clearly A.
Answer: (A) 88.8
Question: If a sample of data has mean of 24 and SD of 3, which of the following values is more than 2.5 SDs from the mean?
(A) a. 19
(B) b. 18.5
(C) c. 15
(D) d. 23.5
(E) e. 26.5
Rationale: Value ismore than 2.5SDfrom the mean means that the distance between the mean and the value must be more than 2.5SD=7.5. So the value either <24-7.5=16.5 or >24+7.5=31.5.
Answer: C.
Answer: (C) c. 15
Question: A fruit seller has oranges, apples and guavas in the ratio 2:5:8. The number of apples is more than the number of oranges by a number that is a multiple of both 6 and 11. What is the minimum number of fruits in his shop?
(A) 240
(B) 360
(C) 120
(D) 90
(E) 80
Rationale: DETAILED SOLUTION
Let the number of fruits be 2k, 5k and 8k
Given, 5k – 2k = multiple of 6 and 8
LCM of 6 and 8 is 24
Let’s say 5k – 2k = 24n
3k = 24n
For k to be a natural number and have minimum value, n should be equal to 1
3k = 24
Or k = 8
Hence, the number of fruits = 2k + 5k + 8k
= 15 * 8= 120
Correct Answer:C
Answer: (C) 120
Question: Find the area of the quadrilateral of one of its diagonals is 40 cm and its off sets 9 cm and 6 cm?
(A) 189 cm2
(B) 300 cm2
(C) 127 cm2
(D) 177 cm2
(E) 187 cm2
Rationale: 1/2 * 40(9 + 6)
= 300 cm2
Answer: B
Answer: (B) 300 cm2
Question: A four-character password consists of one letter of the alphabet and three different digits between 0 and 8, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?
(A) 5,040
(B) 18,720
(C) 26,000
(D) 26,208
(E) 52,000
Rationale: 4 character password: DLDD
First digit can be chosen in 9 ways.
The letter can be chosen in 26 ways.
Next digit can be chosen in 8 ways.
Next digit can be chosen in 7 ways.
This gives us 9*26*8*7ways
Now, the letter can also be DDLD so there will be another 9*26*8*7 ways
Total = 9*26*8*7*2 = 26,208 ways D
Answer: (D) 26,208
Question: Tom and Jerry are running on the same road towards each other. If Tom is running at a speed of 2.5 meters per second and Jerry is running 36% slower, how much time T will it take them to meet if the initial distance between the two is 50 meters and Tom started running 20 seconds before Jerry did?
(A) 2 minute and 12 seconds.
(B) two minutes.
(C) 44 seconds.
(D) 20 seconds.
(E) 12 seconds.
Rationale: Tom is running alone for 20 seconds.
So he will cover a distance of 20*2.5 = 50 m in 20 seconds=T
Basically, Jerry has not started yet , and Tom has covered the distance alone and met Jerry on the other side
D is the answer
Answer: (D) 20 seconds.
Question: Find the number of factors of 300 excluding 1 and itself.
(A) 22
(B) 28
(C) 16
(D) 88
(E) 26
Rationale: Explanation:
300 = 4.75 = 4.25.3 = 22.52.31
Number of factors of 300 = (2 + 1)(2 + 1)(1 + 1) = 18.
There are 16 factors of 300 excluding 1 and itself.
Answer: C
Answer: (C) 16
Question: At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 60. If the restaurant serves 120 customers today, raising the average to 70 customers per day, what is the value of x?
(A) 2
(B) 5
(C) 9
(D) 15
(E) 30
Rationale: WITHOUTusing the formula, we can see that today the restaurant served 50 customers above the average. The total amount ABOVE the average must equal total amount BELOW the average. This additional 50 customers must offset the “deficit” below the average of 70 created on the x days the restaurant served only 60 customers per day.
50/10 = 5 days.Choice (A).
WITHthe formula, we can set up the following:
70 = (60x + 120)/(x + 1)
70x + 70 = 60x + 120
10x = 50
x = 5Answer Choice (B)
Answer: (B) 5
Question: Darcy, Gina, Ray and Susan will be the only participants at a meeting. There will be three soft chairs in the room where the meeting will be held and one hard chair. No one can bring more chairs into the room. Darcy and Ray will arrive simultaneously, but Gina and Susan will arrive individually. The probability that Gina will arrive first is 1/3, and the probability that Susan will arrive first is 1/3. The probability that Gina will arrive last is 1/3, and the probability that Susan will arrive last is 1/3. Upon arriving at the meeting, each of the participants will select a soft chair, if one is available.
If Darcy and Ray arrive and see only one unoccupied soft chair, they will flip a fair coin to determine who will sit in that chair. By what percent is the probability that Darcy will sit in a soft chair greater than the probability that Gina will sit in a soft chair?
(A) 50%
(B) 25%
(C) 16 2/3%
(D) 12 1/2%
(E) 0%
Rationale: Location of D to access a soft Chair
If DR comes in first or second place both as R D they will access a soft Chair, this means that D in this situation has 1/3 + 1/3 to a soft Chair.
If DR comes third (last), D has a probability of (1/2) x (1/3) access to a soft Chair.
Then in all cases D has a probability of 1/3 + 1/3 + (1/2) x (1/3) = 5/6 access to a soft Chair.
Location of G to access a soft Chair
To G enter a soft Chair, you can only get in first or second place, if it reaches third we have addressed three soft chairs DR two soft chairs and S a soft Chair.
The probability that G arrives in first or second place is 1/3 + 1/3 = 2/3 = 4/6
Finally the highest percentage who D on G accesses a soft Chair is:
100 x (5/6 - 4/6) /(4/6) = 25%
ANSWER:D
Answer: (D) 12 1/2%
Question: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 2/5 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?
(A) 2/15
(B) 3/15
(C) 4/5
(D) 2/5
(E) 1/5
Rationale: The fraction of homes which are termite-infested but not collapsing is 3/5*1/3 = 1/5
The answer is E.
Answer: (E) 1/5
Question: 16 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?
(A) 32
(B) 87
(C) 30
(D) 99
(E) 77
Rationale: 3W = 2M
16M ------ 21 * 8 hours
21 W ------ x * 6 hours
14 M ------ x * 6
16 * 21 * 8 = 14 * x * 6
x = 32
Answer: A
Answer: (A) 32
Question: If four fair dice are thrown simultaneously, what is the probability of getting at least one pair?
(A) 1/6
(B) 5/18
(C) 1/2
(D) 2/3
(E) 13/18
Rationale: 1st roll = any number = 6/6
2nd roll = not a match to the first = 5/6
3rd roll = not a match to the 1st or 2nd = 4/6
4th roll = not a match to the 1st or 2nd or 3rd = 3/6
(6/6)(5/6)(4/6)(3/6) =
(1)(5/6)(2/3)(1/2) =
10/36
10/36 is the probability of rolling 0 matching numbers, so...
1 - 10/36 = 26/36 = the probability of rolling at least one matching pair of numbers
26/36 = 13/18
Answer:E
Answer: (E) 13/18
Question: The average age 10 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
(A) 14 years
(B) 17 years
(C) 20 years
(D) 12 years
(E) 11 years
Rationale: 10 * 2
= 20
Answer:C
Answer: (C) 20 years
Question: The difference of a larger number and a smaller number is 6. The sum of the larger number and twice the smaller is 15. What is the larger number?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Let x be the larger number and y be the smaller number.
x - y = 6
x + 2(y) = 15
Solve by substitution: y = x - 6
x + 2(x-6)=15
x + 2x -12 = 15
3x = 27
x=9
The larger number is 9, so answer C is correct.
Answer: (C) 9
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
(A) 3/9
(B) 3/2
(C) 3/6
(D) 3/2
(E) 3/9
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.Answer:B
Answer: (B) 3/2