divelab/Sys2Bench huggingface dataset:
Question: 5358 x 53 = ?
Options:
A)272258
B)272358
C)283974
D)274258
E)274358
Rationale: 5358 x 51	= 5358 x (50 + 3)
= 5358 x 50 + 5358 x 3
= 267900 + 16074
= 283974.
C)
Answer: C
Question: Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $360 per week. How much does she earn in dollars per hour?
Options:
A)11
B)10
C)9
D)8
E)7
Rationale: Let Sheila earn x dollars per hour
So, on Monday, Wednesday and Friday , she earns 8x each
And, on Tuesday and Thursday, she earns 6x each
In total , over the week she should earn, 3(8x) + 2(6x) = 36x
She earns $360 per week
36x =360
x =10
Correct Option : B
Answer: B
Question: In what ratio must tea at Rs.62 per Kg be mixed with tea at Rs. 72 per Kg so that the mixture must be
worth Rs. 64.50 per Kg?
Options:
A)1 : 2
B)2 : 1
C)3 : 1
D)1 : 3
E)None of these
Rationale: Explanation :
By the rule of alligation, we have
Cost of 1 kg of 1st kind tea Cost of 1 kg tea of 2nd kind tea
62 72
Mean Price
64.5
72-64.5=7.5 64.5-62=2.5
Required Ratio = 7.5 : 2.5 = 3 : 1
Answer : Option C
Answer: C
Question: An investor can sell her MicroTron stock for 36$ per share and her Dynaco stock for 60$ per share, If she sells 300 shares altogether, some of each stock, at an average price per share of 40$, how many shares of Dynaco stock has she sold?
Options:
A)50
B)75
C)92
D)136
E)184
Rationale: w1/w2 = (A2 - Aavg)/(Aavg - A1) = (60 - 40)/(40 - 36) = 20/4 = 5/1 = Number of MicroTron stocks/Number of Dynaco stocks
So for every 5 MicroTron stock, she sold 1 Dynaco stock.
So out of 300 total stocks, (1/5)th i.e. 300/6 = 50 must be Dynaco stock.
Answer (A)
Answer: A
Question: A box contains four copper coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is also a head.
Options:
A)3/4
B)1/5
C)2/5
D)3/5
E)4/5
Rationale: There are four ways (2 heads in one two-headed coin and 2 heads in the other two-headed coin)
How many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)
Therefore probability = 4/5
Option E
Answer: E
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 6 different boat to go and 4 flight to return. In how many ways, can the boy perform his journey?
Options:
A)20
B)40
C)45
D)60
E)24
Rationale: Ans.(E)
Sol. Number of choices to go by ship = 6 Number of choices to return by airline = 4 From, fundamental principle, total number of ways of performing the journey = 6 x 4 = 24 ways
Answer: E
Question: Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 13 times as heavy as water?
Options:
A)1:2
B)2:3
C)4:1
D)5:2
E)6:5
Rationale: G = 19W
C = 9W
Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy
1gm gold + x gm copper = x+1 gm of alloy
19W+9Wx = x+1 * 13W
19+9x = 13(x+1)
x = 3/2
Ratio of gold with copper = 1:3/2 = 2:3
Answer is B
Answer: B
Question: A certain debt will be paid in 40 installments from January 1 to December 31 of a certain year. Each of the first 20 payments is to be $410; each of the remaining payments is to be $65 more than each of the first 20 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year?
Options:
A)442.5
B)450
C)465
D)468
E)475
Rationale: Total number of installments = 40
Payment per installment for the first 20 installments = 410
Payment per installment for the remaining 20 installments = 410+65=475
Average = (20*410 + 20*475)/40 =442.50
Answer A
Answer: A
Question: Paul sells encyclopedias door-to-door. He earns $80 on every paycheck, regardless of how many sets he sells. In addition, he earns commission as follows:
Commission Sales
10% $0.00 - $10,000.00
5% $10,000.01 --->
He does not earn double commission.That is, if his sales are $12,000, he earns 10% on the first $10,000 and 5% on the remaining $2,000.
His largest paycheck of the year was $1,320. What were his sales for that pay period?
Options:
A)13,200
B)14,800
C)16,400
D)15,800
E)19,600
Rationale: His pay check was $1320.
Out of this, $80 was his fixed salary so the total commission he earned was $1320 - $80 = $1240
He earns 10% on the sales of first $10,000 which gives a commission of $1000.
He earns 5% on every subsequent dollar. Since he earns another $240, he must have had sales of another 240*(100/5) = 4800
So his total sales must have been $10,000 + $4800 = $14,800
B
Answer: B
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9% p.a. in 5 years. What is the sum?
Options:
A)2762
B)2877
C)2882
D)8925
E)2887
Rationale: Principal = (100 * 4016.25) / (9 * 5)
= Rs.8925.
Answer:D
Answer: D
Question: Two right circular cylinders of equal volumes have their heights in the ratio 1:2. Find the ratio of their radii.
Options:
A)√2:6
B)√2:1
C)√2:1
D)√2:2
E)√2:4
Rationale: Let their heights be h and 2h and radii be r and R respectively then.
πr2h=πR2(2h)=>r2R2=2hh=21=>rR=2–√1=>r:R=√2:1
Answer:C
Answer: C
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
Options:
A)11.9
B)11.4
C)11.2
D)11.5
E)11.1
Rationale: 1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 119.9 = 11.5
6th number = 11.5
Answer:D
Answer: D
Question: If the price of gold increases by 40%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
Options:
A)331/8%
B)26.67%
C)28.5%
D)332/3%
E)131/3%
Rationale: 100
140
------
140-------40
100-------? => 28.5%
Answer:C
Answer: C
Question: In a school where there are more than 100 students when they are grouped into 12 and 16, always 6 students remain ungrouped. What would be the minimum number of new students to be registered to this school such that when they are grouped into 20 then none of the stundents remains ungrouped ?
Options:
A)6
B)8
C)9
D)10
E)12
Rationale: S=12a+6=16b+6
6a = 8b --> for S>100 min(a,b) = (12,9)
then number of stundent in school --> 12*12 +6 = 150
20k = 150 + x so that none will be ungrouped --> min( k) = 8 then
20*8 =150 + x
x = 10 new students to be registered
ANSWER: D
Answer: D
Question: A, B and C started a shop by investing Rs. 5,000, Rs. 15,000 and Rs. 30,000 respectively. At the end of the year, the profits were distributed among them. If Câ€™s share of profit be Rs. 3000, then the total profit was :
Options:
A)30,000
B)5,000
C)80,000
D)120,000
E)None
Rationale: Sol.
A : B : C = 5000 : 15000 : 30000 = 1: 3 : 6. so, Câ€™s share : Total Profit = 6 : 10
Let the total profit be Rs. x. Then, 6/10 = 3000/x or x
= 3000 * 10 /6 = 5000.
Answer B
Answer: B
Question: Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/6 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?
Options:
A)0
B)1/12
C)2/15
D)1/10
E)2/10
Rationale: Suppose the water in each jug is L liters
CX x (1/6) = L
CX = 6L liters
CX is capacity of X
CY x (2/3) = L
CY = 3L/2 liters
CY is capacity of Y
Now, Y is 3L/2 - L empty = L/2 empty
So, we can put only L/2 water in jug Y from Jug X
Jug X's remaining water = L - L/2 = L/2
Fraction of X which contains water = water / CX
= (L/2)/ 6L
= 1/12
Answer will be B
Answer: B
Question: In a apartment, 30% of the people speak English, 20% speak Hindi and 11% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
Options:
A)1/30
B)12/13
C)16/41
D)12/91
E)13/71
Rationale: P (E) = 30 / 100 , P (H) = 20 / 100 and P (E âˆ© H) = 11 / 100 =
P (E or H) = P (E U H)
= P (E) + P (H) - P (E âˆ© H)
= (30 / 100) + (20/100 - (11 / 100) = 39/100 = 16/41
C
Answer: C
Question: A satellite is composed of 24 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/3 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?
Options:
A)5/6
B)1/5
C)1/6
D)1/9
E)1/24
Rationale: Let x be the number of upgraded sensors on the satellite.
The number of non-upgraded sensors per unit is x/3.
The number of non-upgraded sensors on the whole satellite is 24(x/3) = 8x.
The fraction of sensors which have been upgraded is x / (x+8x) = x/9x = 1/9
The answer is D.
Answer: D
Question: Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 44 kmph respectively. In how much time will they cross each other, if they are running in the same direction?
Options:
A)140 sec
B)132 sec
C)192 sec
D)252 sec
E)None
Rationale: Solution
Relative Speed	= (44 - 40 ) Kmph
= 4 kmph
=(4 x 5 / 18)m/sec
= (20 / 18 ) m/sec
Time taken	= (350 x 18 / 20) sec
= 140 sec.
Answer A
Answer: A
Question: Boy sells a book for Rs. 450 he gets a loss of 10 %, To gain 10 %, what should be the SP?
Options:
A)Rs.330
B)Rs.430
C)Rs.550
D)Rs.600
E)Rs.620
Rationale: Find Selling Price to gain 10 %.
Now, we are asked to find selling price to gain 10% profit.
Hint:
Selling Price = (100 + Gain%) × C.P.
100
Selling Price = (100 + 10) × 500
100
Selling Price = (110) × 500
100
Therefore, selling Price = Rs.550
C
Answer: C
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
Options:
A)9
B)8
C)7
D)6
E)4
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Answer: B
Question: The average of runs of a cricket player of 20 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options:
A)96
B)106
C)122
D)116
E)122
Rationale: Average = total runs / no.of innings = 32
So, total = Average x no.of innings = 32 * 20 = 640
Now increase in avg = 4 runs. So, new avg = 32+4 = 36 runs
Total runs = new avg x new no. of innings = 36 * 21 = 756
Runs made in the 11th inning = 756-640 = 116
ANSWER:D
Answer: D
Question: What is the sum of all possible solutions to |x - 4|^2 + |x - 4| = 20 ?
Options:
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
Question: If f(x) = ax^2 – 6x + ax + 1, then f(b) – f(-b) will equal:
Options:
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
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?
Options:
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
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?
Options:
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
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
Options:
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
Question: What is the sum of all possible solutions to |x - 6|^2 + |x - 6| = 20 ?
Options:
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
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 ?
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
Question: If two dice are thrown simultaneously, then find the probability that the sum of numbers appeared on the dice is 3?
Options:
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
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.
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
Question: If the quotient a/b positive, which of the following must be true?
Options:
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
Question: If you take 3 apples from a group of 5, how many do you have?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: C
Three - you just took them yourself!
Answer: C
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?
Options:
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
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?
Options:
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
Question: What is the are of an equilateral triangle of side 12 cm?
Options:
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
Question: At what time between 4 and 5 o'clock will the hands of a clock be at right angle?
Options:
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
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 ?
Options:
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
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.
Options:
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
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 :
Options:
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
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?
Options:
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
Question: In how many ways can the letters of the word RECPECT be arranged?
Options:
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
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?
Options:
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
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?
Options:
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