mathewhe/aqua_rat huggingface dataset:
Question: What is the sum of all possible solutions to |x - 4|^2 + |x - 4| = 20 ?
(A) -1
(B) 6
(C) 7
(D) 8
(E) 14
Rationale: Denote |x - 4| as y: y^2 + y = 20 --> y = -5 or y = 4. Discard the first solution since y = |x - 4|, so it's an absolute value and thus cannot be negative.
y = |x - 4| = 4 --> x = 8 or x = 0. The sum = 8.
Answer: D.
Answer: (D) 8
Question: If f(x) = ax^2 – 6x + ax + 1, then f(b) – f(-b) will equal:
(A) 0
(B) -12b+2ab
(C) 2ab^4 – 8b^2 – 6
(D) -2ab^4 + 8b^2 + 6
(E) 2ab^4 – 8b^2 + 2ab – 6
Rationale: f(x)=ax^2 – 6x + ax + 1
f(b) = ab^2 – 6b + ab + 1
f(-b) = ab^2 + 6b - ab + 1
f(b) - f(-b) = ab^2 – 6b + ab + 1 - ab^2 - 6b + ab - 1
=-12b+2ab
Answer B
Answer: (B) -12b+2ab
Question: Jim goes 6.4 mph on his bike. He needs to go to the store to get bread. The store is 2 miles away if he leabes now at 2 pm what time will he return if it takes him 13 minutes in the store?
(A) 2 hr 4 m
(B) 1 h 15 m
(C) 1 hr 37 m
(D) 1 hr 24 m
(E) 2 hr 45 m
Rationale: 31 minutes each way (6.4/2) +31 minutes + 13 min in store =1 hr 15 m
Correct answer B
Answer: (B) 1 h 15 m
Question: A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60º. What is the distance between the base of the tower and the point P?
(A) 9.2 m
(B) 9.9 m
(C) 3.2 m
(D) 9.8 m
(E) 7.2 m
Rationale: Let AB be the wall and BC be the ladder.
Then, ACB = 60º and AC = 4.6 m.
AC	= cos 60º =	1
BC	2
BC	= 2 x AC
= (2 x 4.6) m
= 9.2 m.
Answer:A
Answer: (A) 9.2 m
Question: A vendor sold two things at same cost of 14 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much
(A) 0.60 loss
(B) 0.70 loss
(C) 0.80 loss
(D) 0.50 loss
(E) 0.40 loss
Rationale: CP when profit of 25% = 11.2
CP when loss of 20% = 17.5
Total CP = 28.7
Total SP = 28.00
Total loss = 0.70
ANSWER:B
Answer: (B) 0.70 loss
Question: What is the sum of all possible solutions to |x - 6|^2 + |x - 6| = 20 ?
(A) -1
(B) 6
(C) 7
(D) 12
(E) 14
Rationale: Denote |x - 6| as y: y^2 + y = 20 --> y = -5 or y = 4. Discard the first solution since y = |x - 6|, so it's an absolute value and thus cannot be negative.
y = |x - 6| = 4 --> x = 10 or x = -2. The sum = 12.
Answer: D.
Answer: (D) 12
Question: A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 42 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?
(A) 48pi/x
(B) 75x
(C) 40x
(D) 24x
(E) x/75
Rationale: It's C.
Let's try the explanation. We have two wheels. One with 28pi and the other one with 42pi. They have the same speed. In the smaller wheel it's 28pi*x, which must be equal to the speed of the bigger one (42pi*a number of revolutions).They are asking that number of revolutions (but in minutes, which makes the question even harder).
Anyway, we have 28pi*x=42pi*a.
(28pi*x)/(42pi). As I said, that's in seconds. So, to convert it to minutes we multiply by 60 and we get the result, 40x.
Ans : C
Answer: (C) 40x
Question: There is a train and car. The ratio btw the speed of a train & a car is 16:15 respectively. Also, a bus covered a distance of 480km in 8h. The speed of the bus is 3/4th of the speed of the train. How much distance will the car cover in 6h?
(A) 340 km
(B) 360 km
(C) 400 km
(D) 420 km
(E) 450 km
Rationale: Sol. Speed of bus = 480/8 = 60km/ h
Speed of train = (60*4)/3=80 km / h
Speed of train : Speed of car = 16 : 15
Speed of car =80/16 * 15 = 75 km/ h
Distance covered by car in 6 hr = 75 × 6 = 450 km
E
Answer: (E) 450 km
Question: 2 metres broad pathway is to be constructed around a rectangular plot on the inside. The area of the plots is 96 sq.m. The rate of construction is Rs. 50 per square metre. Find the total cost of the construction?
(A) Rs.2400
(B) Rs.4000
(C) Data inadequate
(D) None of these
(E) Cannot be determined
Rationale: Solution
Given lb =96
Area of pathway	= [(l-4)(b-4)-lb]
= 16-4(l+b)
Which cannot be determined. so, data is inadequate.
Answer C
Answer: (C) Data inadequate
Question: Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 160 sandwiches were made, how many bologna sandwiches
were made?
(A) 15
(B) 30
(C) 38
(D) 56
(E) 48
Rationale: For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts
and we should calculate how many sandwiches holds 1 part:
160 / 20 = 8 sandwiches in one part
For bologna we have 7 parts so:
7 * 8 = 56
Answer is D
Answer: (D) 56
Question: If two dice are thrown simultaneously, then find the probability that the sum of numbers appeared on the dice is 3?
(A) 5/6
(B) 7/36
(C) 5/36
(D) 2/36
(E) 12/36
Rationale: The sum of numbers appeared is 3.
Therefore, the required probability = n(E)/n(S) = 2/36.
ANSWER:D
Answer: (D) 2/36
Question: if A and B run on a circular path in opposite directions of constant speeds with different velocities from P and Q. First time they meet 800 mts away from P and second time they meet 700 mts away from P, what is the lenght of the circular path.
(A) 2300 Mtrs
(B) 2400 Mtrs
(C) 2500 Mtrs
(D) 2600 Mtrs
(E) 2700 Mtrs
Rationale: 800 +800+700= 2300 Mtrs
ANSWER:A
Answer: (A) 2300 Mtrs
Question: John was 43 years old when he married Betty. They just celebrated their fifth wedding anniversary, and Betty's age is now 7/8 of John's. How old is Betty?
(A) 24
(B) 26
(C) 42
(D) 30
(E) 32
Rationale: Assume Betty's age on marriage = x years.
John's age on marriage = 43
John's age after 5 years = 48 years.
Betty's age after 5 years = x + 5
Given: x + 5 = 7/8 (48) = 42
Therefore Betty's current age = 42
Option C
Answer: (C) 42
Question: There are 10 points on a circle. A hexagon can be formed by linking 7 of the 10 points. How many such hexagons are possible?
(A) 60
(B) 120
(C) 200
(D) 210
(E) 600
Rationale: 7 points can be selected out of 10 points in 10C7 ways
=10 !/7!*3!=120
Ans B
Answer: (B) 120
Question: In a hostel, the number of students decreased by 5% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?
(A) 19%
(B) 12.3%
(C) 25%
(D) 40%
(E) 9.4%
Rationale: Cost of food (C) = Food consumed per student (F) * Number of students (N) * Price of food (P)
Originally,
C = FNP
When number of students decrease by 5%, and the price of food increases by 20%,
C = F(new) * (0.95N) * (1.2P)
=> F(new) = F/(0.95*1.2)
=> F(new) = 0.877F
Therefore the new cost of food must be 87.7% of the old cost, or the cost of food must decrease by 12.28% (optionB)
Answer: (B) 12.3%
Question: Mona and Donald fly to Rome for the weekend. They take cash only in notes of $10 and notes of €10. Mona carries three times the amount of euros Donald carries. She also carries as many dollars as Donald carries. The number of €10 notes they take is double the number of $10 notes they take. If Donald carries a total of 33 notes (of either $10 or €10,) then what is the total number of notes (of either $10 or €10,) they take?
(A) 70
(B) 110
(C) 100
(D) 120
(E) 150
Rationale: let e10 =x no. d10 =y no. donald is having x+y notes mona carries 3x+y again x =2y or donald x+y =33
or 3y =33 y =11 ;x =22 , total notes they carry = 4x+2y = 88+22 =110
B
Answer: (B) 110
Question: If the quotient a/b positive, which of the following must be true?
(A) a > 0
(B) b > 0
(C) ab > 0
(D) a-b > 0
(E) a+b > 0
Rationale: a/b>0 means aa and bb have the same sign, either both are negative or both are positive. Thus, their product will also be positive: ab>0.
Answer: C.
Answer: (C) ab > 0
Question: If you take 3 apples from a group of 5, how many do you have?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: C
Three - you just took them yourself!
Answer: (C) 3
Question: Last year Department Store X had a sales total for December that was 3 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?
(A) 1/4
(B) 4/15
(C) 3/14
(D) 4/11
(E) 4/5
Rationale: Let avg for 11 mos. = 10
Therefore, Dec = 30
Year total = 11*10 + 30 = 140
Answer = 30/140 = 3/14 = C
Answer: (C) 3/14
Question: A and B can do a piece of work in 60 days and 60 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed?
(A) 30days
(B) 35days
(C) 40days
(D) 45days
(E) 50days
Rationale: Explanation:
(A+B)’s 10 days work = 10[1/60+1/60]=10[1+1/60]= 1/3
A complete remaining work in 1/3*60 = 20
Total work = 10+20 = 30days
Answer: Option A
Answer: (A) 30days
Question: What is the are of an equilateral triangle of side 12 cm?
(A) 64√5
(B) 64√9
(C) 64√4
(D) 36√3
(E) 64√2
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 12, Area of triangle = √3/4 * 12 * 12 = 36√3 cm2;
Answer: D
Answer: (D) 36√3
Question: At what time between 4 and 5 o'clock will the hands of a clock be at right angle?
(A) 30/11 min. past 4.
(B) 30/11 min. past 5.
(C) 40/11 min. past 4.
(D) 25/11 min. past 4.
(E) 37/11 min. past 4.
Rationale: Sol: At 4 o'clock, the minute hand will be 20 min. spaces behind the hour hand, Now, when the two hands are at right angles, they are 15 min. spaces apart. So, they are at right angles in following two cases.
Case I. When minute hand is 15 min. spaces behind the hour hand:
In this case min. hand will have to gain (20 - 15) = 5 minute spaces. 55 min. spaces are gained by it in 60 min.
5 min spaces will be gained by it in 60*5/55 min=60/11min.
:. They are at right angles at 60/11min. past 4.
Case II. When the minute hand is 15 min. spaces ahead of the hour hand:
To be in this position, the minute hand will have to gain (20 + 15) = 35 minute spa' 55 min. spaces are gained in 60 min.
35 min spaces are gained in (60 x 35)/55 min =40/11
:. They are at right angles at 40/11 min. past 4.
Answer is C.
Answer: (C) 40/11 min. past 4.
Question: An industrial loom weaves 1.14 meters of cloth every second. Approximately, how much time will it take to weave 52 meters of cloth ?
(A) 29.32 sec
(B) 42.51 sec
(C) 39.25 sec
(D) 45.61 sec
(E) None of these
Rationale: Explanation:
Given loom weaves 1.14 mts of cloth in one second then 52 mts of cloth can be weaved by loom in,
1.14 ----- 1
52.0 ------?
=> 52/1.14 = 45.61 sec
Answer IS D
Answer: (D) 45.61 sec
Question: In a survey conducted to find out the readership of three Newspapers A,B and C, it was found that the number of newspaper A is at least 20 and at most 40. The number of people who read newspaper B is at least 50 and at most 70. The number of people who read newspaper C is at least 70 and at most 83. It was also found that 10 people read all three newspapers. Find the minimum number of people who read both A and B but not C.
(A) A)1
(B) B)2
(C) C)3
(D) D)0
(E) E)5
Rationale: I wish I could draw a diagram to show you but by giving you number A and B, it might help a little.
A and B and C is 10 - that means A and B is at least 10. This seems trivial given the value intervals of A and B but definitely helps to think through how to minimize A and B but not C
A and B but not C = |A|-|B| - 10
So i would pick A=50 and B =50 to minimize the value to a 0. (ANS D)
Answer: (D) D)0
Question: A dog takes 5 leaps for every 8 leaps of a hare. If one leap of the dog is equal to 4 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
(A) 5:8
(B) 5:3
(C) 5:2
(D) 5:9
(E) 2:5
Rationale: Explanation:
Dog : Hare = (5*4) leaps of hare :8 leaps of hare = 20 : 8--> 10:4-->5:2
Answer: C
Answer: (C) 5:2
Question: My cat keeps to himself most of the time. I only heard him meow, hiss, and purr on one day
out of the last 23 days. But I did hear him make at least one of these sounds each day. I heard
him hiss on 6 days, purr on 12 days, and meow on 15 days. On 2 days, I heard him meow and
hiss but not purr, and on 2 days, I heard him purr and hiss but not meow. On how many days
did I hear him meow and purr but not hiss?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Let M denote the days on which the cat meowed, H the days on which he hissed,
and P the days on which he purred. Given the data, the following Venn diagram represents
the situation, where the expressions inside the circles are the cardinalities of disjoint sections:
We are looking for x. The labeled sections of the Venn diagram are disjoint sets, so they
should add to 23. That is,
23 = 1 + 1 + 2 + 2 + x + (9 􀀀 x) + (12 􀀀 x) = 27 􀀀 x:
Therefore,x = 4.
or
The inclusion-exclusion principle gives
23 = jM [ H [ Pj = jMj + jHj + jPj 􀀀 jM \ Hj 􀀀 jH \ Pj 􀀀 jM \ Pj + jM \ H \ Pj
= 15 + 6 + 12 􀀀 (2 + 1) 􀀀 (2 + 1) 􀀀 (x + 1) + 1:
So x = 4.
correct answer D
Answer: (D) 4
Question: In how many ways can the letters of the word RECPECT be arranged?
(A) 1206
(B) 1348
(C) 2520
(D) 3000
(E) 3478
Rationale: RECPECT has 7 words, but E is repeated two times. Thus ways = 7! / 2! = 2520 ways
C
Answer: (C) 2520
Question: Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 216 marks in the second test and failed by 36 marks in that test. Find the pass mark in the first test?
(A) 136
(B) 128
(C) 164
(D) 214
(E) 224
Rationale: Let the maximum mark in each test be M.
The candidate failed by 36 marks in the second test.
pass mark in the second test = 216 + 36 = 252
45/100 M = 252
Pass mark in the first test = 40/100 M = 40/45 * 252 = 224.
ANSWER:E
Answer: (E) 224
Question: A sum fetched a total simple interest of Rs. 144 at the rate of 15 p.c.p.a. in 1 year 6 months. What is the sum?
(A) 490
(B) 850
(C) 580
(D) 640
(E) 760
Rationale: Sol.
Principal = Rs. [100 * 144 / 15 * (18/12)] = Rs. [14400 / 22.5] = Rs. 640.
Answer D
Answer: (D) 640
Question: Paige had a nature collection. She had 25 acorns, 16 dried seed pods, and 8 feathers. She
divided the acorns into 5 equal groups, the seed pods into 4 equal groups and the feathers into 2
equal groups. She gave her mother one group of each kind. How many separate items did her
mother get?
(A) 23 items
(B) 33 items
(C) 13 items
(D) 3 items
(E) 43 items
Rationale: 25 ÷ 5 = 5 acorns in a group
16 ÷ 4 = 4 seed pods in a group
8 ÷ 2 = 4 feathers in a group
5 + 4 + 4 = 13 items given to Mom
correct answer C
Answer: (C) 13 items
Question: Find 40 % of 440
(A) 96
(B) 94
(C) 86
(D) 176
(E) 110
Rationale: We know that R % of m is equal to R/100 × m.
So, we have 40 % of 440
40/100 × 440
= 176
Answer:D
Answer: (D) 176
Question: The value of (10^8-10^2)/(10^4-10^3) is closest to which of the following?
(A) 1
(B) 10
(C) 10^2
(D) 10^3
(E) 10^4
Rationale: Because the question asks for what value isclosestthe question invites approximation.
Let's look at the numerator:
10^8 - 10^2
10^8 is HUGE compared to 10^2.
So 10^8 - 10^2 is very close to 10^8 itself. (Just as 100 - 0.0001 is very close to 100 itself).
Likewise, 10^4 is HUGE compared to 10^3.
So 10^4 - 10^3 is very close to 10^4.
So we have:
10^8/10^4
or 10^(8-4) = 10^4.
Choose E.
Answer: (E) 10^4
Question: John started driving on a highway at a constant speed of R miles per hour at 13:00. Then, 2 hours later, Tom started driving on the same highway at a constant speed of 5R/3 miles per hour at 15:00. If both drivers maintained their speed, how many miles had John driven on the highway when Tom caught up with John?
(A) 3R
(B) 5R
(C) 8R
(D) 9R
(E) 10R
Rationale: In 2 hours, John drove 2R miles.
Tom can catch John at a rate of 5R/3 - R = 2R/3 miles per hour.
The time it takes Tom to catch John is 2R / (2R/3) = 3 hours.
In 3 hours, John can drive another 3R miles for a total of 5R miles.
The answer is B.
Answer: (B) 5R
Question: Can you replace the question mark with the number to complete the series, provided the pair of numbers exhibits a similar relationship ?
? : 4623 :: 9 : 647
(A) ?= 17
(B) 18
(C) 13
(D) 10
(E) 20
Rationale: A
17
The relationship holds for below formula :
pow(x,3) - pow(x,2) - 1
=> 9*9*9 - 9*9 - 1
=> 729 - 81 - 1
=> 647
Similarly,
17*17*17 - 17*17 - 1
=> 4913 - 289 - 1
=> 4623
Answer: (A) ?= 17
Question: Jonathan’s grandparents lend $1,000 to Jonathan at a simple annual interest rate of 10%. He pays them back 5 years later. How much do they receive?
(A) 1,000∗0.1^5
(B) 1,000∗0.5
(C) 1,000∗1.5
(D) 1,000∗1.1^5
(E) (1,000∗0.1)^5
Rationale: 1>Simple Interest Vs Compound interest (there are answers options with compounded interest)
S.I = P x R x T formula in school the question is asking for Amount in 5 years. so (c) 1,000∗ 1.5
Ans : C
Answer: (C) 1,000∗1.5
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 4 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
(A) 60 gallons
(B) 100 gallons
(C) 120 gallons
(D) 160 gallons
(E) 130 gallons
Rationale: Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 4 gallons\
Volume of whole = 4 * 40 = 160 gallons.
ANSWER:D
Answer: (D) 160 gallons
Question: The sum of the present ages of a father and his son is 62 years. Six years ago, father's age was four times the age of the son. After 6 years, son's age will be:
(A) 12 years
(B) 14 years
(C) 18 years
(D) 20 years
(E) 22 years
Rationale: Let the present ages of son and father be x and (62 - x) years respectively.
Then, (62 - x) - 6 = 4(x - 6)
56 - x = 4x - 24
x = 16
The son's age after 6 years will be 22.
The answer is E.
Answer: (E) 22 years
Question: A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum?
(A) 2099
(B) 6086
(C) 2976
(D) 2000
(E) 3862
Rationale: P(11/10)4 - P(6/5)2
= 482
P = 2000
Answer:D
Answer: (D) 2000
Question: Sonika deposited Rs.6000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
(A) 9680
(B) 2277
(C) 2999
(D) 9560
(E) 1212
Rationale: (6000*3*2)/100 = 360
9200
--------
9560
Answer:D
Answer: (D) 9560
Question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much
Look at this series: 1.5, 2.0, 2.5, 3.0, ... What number should come next?
(A) 4.7
(B) 3.5
(C) 4.9
(D) 5.0
(E) 4.4
Rationale: 3.5
In this simple addition series, each number increases by 0.5
Answer : B
Answer: (B) 3.5
Question: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical R present. If the concentration of chemical R is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
(A) 100% decrease
(B) 50% decrease
(C) 40% decrease
(D) 40% increase
(E) 50% increase
Rationale: Let A and R be the concentratrations of the individual chemicals.
Rate of chemical reaction = A^2/R
Since new R is increased by 100%
Rate = A^2/(2R)
For the rate to be constant, new value of A should be square root(2)
So new value of A = 1.414A
That means A is increased by 41.4%
Nearest solution is D
Answer: (D) 40% increase
Question: Applying VBODMAS rule
(A) 31/120
(B) 31/129
(C) 31/1276
(D) 31/122
(E) 31/111
Rationale: Answer:A
Answer: (A) 31/120
Question: P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
(A) 17:5
(B) 17:0
(C) 17:8
(D) 17:1
(E) 17:3
Rationale: P:Q = 85000 : 15000
= 17:3.
Answer: E
Answer: (E) 17:3
Question: If the equation x^2−6x=-2k has at least one solution, which of the following must be true?
(A) k > 9
(B) k < −9
(C) k = 9
(D) k ≤ 9/2
(E) k ≥ −9
Rationale: x^2−6x=-2k
=> x^2−6x + 2k = 0
For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative.
b^2-4ac ≥0
=> 36 - 4*1*(2k) ≥0
=> 36 - 8k ≥0
=> k ≤ 9/2
Answer D
Answer: (D) k ≤ 9/2
Question: A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $2200, what will be C's share of the earnings?
(A) $488.9
(B) $480.9
(C) $588.9
(D) $680.9
(E) $788.9
Rationale: The dollars earned will be in the same ratio as amount of work done
1 day work of C is 1/12 (or 2/24)
1 day work of the combined workforce is (1/6 + 1/8 + 1/12) = 9/24
C's contribution is 2/9 of the combined effort
Translating effort to $ = 2/9 * 2200 = $488.9
hence:A
Answer: (A) $488.9
Question: When positive integer G is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when G is divided by B?
(A)  13
(B)  14
(C)  15
(D)  16
(E)  17
Rationale: the remainder will be obtained from the decimal part when G is divided by B i.e. 0.35
0.35 = 35/100 = 7/20 so possible remainders are 7,14,21,28. Only option B-14 satisfies this
PS: for B-14 G=174 and B=40
Answer: (B)  14
Question: A student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
(A) 27
(B) 26
(C) 218
(D) 80
(E) 18
Rationale: Given M + P + C = 80 * 3 = 240 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 240 = 80
Answer: D
Answer: (D) 80
Question: (?) - 19657 - 33994 = 9999
(A) 63630
(B) 63620
(C) 63670
(D) 63650
(E) 63690
Rationale: D
63650
19657+33994=53651
Let x - 53651 = 9999
Then, x = 9999 + 53651 = 63650
Answer: (D) 63650
Question: P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 15 days to complete the same work. then Q alone can do it in
(A) 20
(B) 22
(C) 25
(D) 27
(E) 60
Rationale: Work done by P and Q in 1 day = 1/10
Work done by R in 1 day = 1/15
Work done by P, Q and R in 1 day = 1/10 + 1/15= 1/6
But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as Work done by P in 1 day Ã— 2 = 1/6
=> Work done by P in 1 day = 1/12
=> Work done by Q and R in 1 day = 1/12
Hence work done by Q in 1 day = 1/12 â€“ 1/15 = 1/60
So Q alone can do the work in 60 days
Answer is E.
Answer: (E) 60
Question: Because he’s taxed by his home planet, Mork pays a tax rate of 40% on his income, while Mindy pays a rate of only 30% on hers. If Mindy earned 3 times as much as Mork did, what was their combined tax rate?
(A) 32.5%
(B) 34%
(C) 35%
(D) 36%
(E) 37.5%
Rationale: Say Morks income is - 100
So tax paid will be 40
Say Mindy's income is 3*100 = 300
So tax paid is 30% * 300 = 90
Total tax paid = 40+90 = 130.
Combined tax % will be 130/100+300 = 32.5%
ANSWER:A
Answer: (A) 32.5%
Question: The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is
(A) 1.2 km
(B) 1.8 km
(C) 2.4 km
(D) 3.6 km
(E) None
Rationale: Solution
Speed downstreams	=(15 + 3)kmph
= 18 kmph.
Distance travelled	(18 x 12/60)km
= 3.6km.
Answer D
Answer: (D) 3.6 km
Question: In how many ways can 10 books be arranged on a shelf such that a particular pair of books should always be together?
(A) 9! x 2!
(B) 5!
(C) 3!
(D) 9!
(E) 2!
Rationale: We have a total of 10 books.
Given that a particular pair of books should always be together. Hence, just tie these two books together and consider as a single book.
Hence we can take total number of books as 9. These 9 books can be arranged in 9P9 =9!=9! ways.
We had tied two books together. These books can be arranged among themselves in 2P2 =2!=2! ways.
Hence, required number of ways
=9!×2!
Ans: A
Answer: (A) 9! x 2!
Question: In a BCCI meeting there are ten people. All shake hands with each other once. How many handshakes will be there altogether?
(A) 28
(B) 9
(C) H
(D) H19
(E) 181
Rationale: Answer:B
Answer: (B) 9