divelab/Sys2Bench huggingface dataset:
Question: A’s speed is 32/27 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
Options:
A)5/32
B)5/27
C)1/27
D)1/32
E)27/32
Rationale: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.
This is what the beginning of the race will look like:
(Start) A_________B______________________________
If A covers 32 meters, B covers 27 meters in that time. So if the race is 32 meters long, when A reaches the finish line, B would be 5 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 5 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 32 meters) would be the same as the time required by B (to cover 27 meters) to reach the finish line.
So B should get a head start of 5/32 th of the race.
Answer (A)
Answer: A
Question: There are 4 numbers W, X, Y, and Z. If W:X = 4/5, X:Y = 5/6, Y:Z = 6/7, then W:Z will be?
Options:
A)4 : 5
B)2 : 3
C)4 : 7
D)1 : 2
E)5 : 7
Rationale: Solution
W : X = 4 : 5, X : Y = 5 : 6, Y : Z = 6 : 7
âˆ´Wâˆ¶Xâˆ¶Yâˆ¶Z= 4 : 5 : 6 : 7.
Thus, W : Z = 4 : 7
Correct Option C
Answer: C
Question: The difference between compound and simple interest on a particular sum of money for 3 years at 6 and 2/3% p.a is Rs.184. What is the sum?
Options:
A)13000
B)13500
C)14000
D)14500
E)15000
Rationale: P = (184*10^6) / (6 2/3 * 6 2/3*(300*6 2/3))
==> 13500
ANSWER B
Answer: B
Question: Four dice are thrown simultaneously. Find the probability that all of them show the same face.
Options:
A)1/45
B)1/35
C)1/216
D)4/216
E)6/216
Rationale: The total number - four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let X be the event that all dice
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability, = 6/6^4
==>1/216
ANSWER C
Answer: C
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 2 a rupee. Find his net profit or loss percent?
Options:
A)100 %
B)200 %
C)250%
D)300%
E)50%
Rationale: The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 2 a rupee, his SP = 4
Profit = SP - CP = 4 - 2 = 2
Profit Percent = 2/2 * 100 = 100 %
Answer:A
Answer: A
Question: A carpenter makes 2 bunk beds every day. A military school needs to organize a place to sleep for 143 soldiers. If there are 5 carpenters working on the job, how many whole days in advance should they receive the order and start working in order to finish the right number of beds assuming that each bunk- bed is used by two soldiers?
Options:
A)3.
B)4.
C)5.
D)6.
E)7.
Rationale: I believe it is C because if 1C makes 3 beds in 1 day then:
1C's rate = 3/1
So 5c's = 3/1 * 5 = 15/1 = 15 beds in a day.
Since we have 173 soldiers who need beds and bunk beds come in pairs, 72 is the least amount of beds needed.
Time = Amount / Rate
Time = 72 / (15/1) = 72/15, simplifying we get 72/15 = 24/5 = 3.8
So, in order for the carpenters to be able to finish they need 4 whole days. At first I made the mistake of thinking how many whole days it took them to finish (as in ignore the partial day) but the prompt clarifiesdays in advance, meaning how many days would they need to finish so even if they finish early, theyusedthat day.
B
Answer: B
Question: If (n + 2)! = 2550 (n!); find ’n’
Options:
A)38
B)35
C)49
D)43
E)34
Rationale: (n + 2)! = 2550(n!)
(n + 2)(n + 1)(n!) = 2550(n!)
(n + 2)(n + 1) = 2550
2n + 3n + 2 - 2550 = 0
2n + 3n - 2548 = 0
2n + 52n - 49n - 2548 = 0
n(n - 49)(n + 52) = 0
n = 49 or n = - 52
ANSWER:C
Answer: C
Question: What is the place value of 5 in the numeral 4529
Options:
A)200
B)300
C)500
D)600
E)700
Rationale: 5*100 = 500
ANSWER C
Answer: C
Question: In a certain country, 60 percent of the population likes basketball, and 34 percent of the population likes both basketball and golf. What percentage of the people who like basketball also like golf?
Options:
A)20%
B)33%
C)40%
D)57%
E)67%
Rationale: Correct Answer: (D).
Since this is a percent problem without concrete numbers, we can assign our own. If we assume that there are 100 people in the country, then 60 people like basketball, and 34 people like basketball and golf. We’re looking for people who like both divided by people who like basketball, so 34/60 = 57%, or choice D.
Answer: D
Question: An auction house charges a commission of 16% on the first $50,000 of the sale price of an item, plus 10% on the amount of of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000?
Options:
A)$115,000
B)$160,000
C)$210,000
D)$240,000
E)$365,000
Rationale: Say the price of the house was $x, then 0.16*50,000+0.1*(x-50,000)=24,000 --> x=$210,000 (16% of $50,000 plus 10% of the amount in excess of $50,000, which is x-50,000, should equal to total commission of $24,000).
Answer: C.
Answer: C
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 240. The amount of the bill is
Options:
A)2200
B)2240
C)1600
D)1354
E)None of these
Rationale: Explanation:
Let P.W. be Rs.x.
Then, S.I. on Rs. x at 16% for 9 months = Rs. 240.
x Ã— 16 Ã— (9/12) Ã— (1/100) = 240 or x = 2000.
P.W. = Rs. 2000.
Sum due = P.W. + T.D. = Rs.(2000
240) = Rs. 2240.
Answer: B
Answer: B
Question: If you cut a 30ft piece of wood into two pieces making one piece 4ft longer than the other. What size is the smaller piece?
Options:
A)4ft
B)6ft
C)8ft
D)10ft
E)13ft
Rationale: Total length is 30ft, one piece is 4ft longer (x+4), leaving the other piece to figure out (x).
(x)+ (x+4)=30
x+x+4-4=30-4
2x=26
2x/2=26/2
x=13
The piece is E) 13ft.
Answer: E
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 48 years. What will be the age of the B ten years hence?
Options:
A)39
B)23
C)28
D)96
E)26
Rationale: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 48 => b + c = 96 --- (2)
Answer: D
Answer: D
Question: The avg weight of A,B & C is 60 kg. If D joins the group, the avg weight of the group becomes 65 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 64 kg. What is the weight of A?
Options:
A)56
B)65
C)75
D)89
E)87
Rationale: A + B + C = 3 *60 = 180
A + B + C + D = 4 * 65 = 260 ---- (i)
So, D = 80& E = 80 + 3 = 83
B + C + D +E = 64 * 4 = 256 --- (ii)
From Eq. (i) & (ii)
A-E = 260 – 256 = 4
A = E +4 = 83 + 4 = 87
Answer : E
Answer: E
Question: If 3y + x > 2 and x + 2y <= 3 , What can be said about the value of y?
Options:
A)y = 1
B)y >1
C)y > -2
D)y > -1
E)None of these
Rationale: Explanation :
3y + x > 2 -----(1)
x + 2y < = 3
=> x + 2y + y < = 3 + y
=> x + 3y < = 3 + y -----(2)
From (1)&(2)
2 < 3y + x < 3 + y
=> 2 < 3 + y
=> -1 < y
=> y > -1
Hence (D) is the correct answer.
Answer : D
Answer: D
Question: If the sum of 7 consecutive negative integers is -70, what is the value of the 2nd number in the sequence?
Options:
A)8
B)-9
C)-8
D)9
E)6
Rationale: if sum is -70, the average = median = -70/7 = -10 = which is the middle in the sequence.
7/2 = 3.5. When rounded up = 4. So -10 is the 4th in the sequence.
4th - 2nd = 2 numbers away.
-10 + 2= -8
Answer: C
Answer: C
Question: Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. Seven years from today, the difference between the age of the boy and the combined ages of the girls will be
Options:
A)1
B)2
C)-3
D)–6
E)–1
Rationale: Approach I (Plugin's)
Girl I ............... Girl II ................ Boy
1 ....................... 1 ........................ 3 (Assume the current ages)
1 + 1 < 3 .......... (Satisfies the given condition)
1 Year later there ages are
2 ....................... 2 ......................... 4
2 + 2 = 4 ............ (Satisfies the given condition)
After 7 years there ages are
8 ....................... 8 ............................ 10
Difference = 10 - (8+8) = 10 - 16 = -6
Answer = D
Answer: D
Question: The speed of three cars in the ratio 3 : 4 : 5. The ratio between time taken by them to travel the same distance is
Options:
A)20 : 15 :92
B)20 : 15 :19
C)20 : 15 :29
D)20 : 15 :11
E)20 : 15 :12
Rationale: Let the speeds of cars be 3x, 4x and 5x kmph
Distance travelled by each car be y km
\inline \therefore Ratio of times taken = \inline \frac{y}{3x}:\frac{y}{4x}:\frac{y}{5x}
= \inline \frac{1}{3}:\frac{1}{4}:\frac{1}{5}
= 20 : 15 :12
Answer:E
Answer: E
Question: It costs $3 for the first 30 minutes to make a collect call. After the first 30 minutes it costs $5 per hour. If a certain customer make a collect call lasting for 4 hours and 30 minutes, how much will it cost her?
Options:
A)$23
B)$25
C)$80
D)$15
E)$12
Rationale: 4 hrs 30 min = 270 min
First 30 min ------> $3
Time left is 240 min...
Now, 60 min costs $ 5
1 min costs $ 5/60
240 min costs $ 5/60*240 = $ 20
So, Total cost will be $20 + $3 = $ 23
The answer will be (A) $23
Answer: A
Question: A positive integer, when divided by 6 gives the remainder 2, and when divided by 8 gives the remainder 4. What is the remainder when the integer is divided by 48?
.
Options:
A)0
B)Between 1 and 6, inclusive
C)Between 7 and 12, inclusive
D)Between 13 and 19, inclusive
E)Greater than or equal to 20
Rationale: Given number = 6n+2 = 8m+4
Start 6n+2 --> 8, 14, 20, 26, 32, 38, 44, 50, 56, 62, 68....
Of these only 20 and 68 fit the description 8m+4.
In both cases the remainder when divided by 48 is 20.
So answer has to be E.
Answer: E
Question: A clock is started at noon. By 10 minutes past 5, the hour hand has turned through
Options:
A)145°
B)150°
C)155°
D)160°
E)None
Rationale: Solution
Angle traced by hour hand in
12 hrs	=360°
Angle traced by hour hand in
5 hrs 10 min	= 31 / 6 hrs
=[360 / 12 x 31 / 6]
= 155°.
Answer C
Answer: C
Question: By selling 50 meters of cloth. I gain the selling price of 14 meters. Find the gain percent?
Options:
A)42 7/7%
B)42 5/8%
C)38 8/9%
D)42 6/8%
E)42 1/7%
Rationale: SP = CP + g
50 SP = 50 CP + 14 SP
36 SP = 50 CP
36 --- 14 CP gain
100 --- ? => 38 8/9%
Answer: C
Answer: C
Question: Machine A and machine B process the same work at different rates. Machine C processes work as fast as Machines A and B combined. Machine D processes work three times as fast as Machine C; Machine D’s work rate is also exactly four times Machine B’s rate. Assume all four machines work at fixed unchanging rates. If Machine A works alone on a job, it takes 7 hours. If all four machines work together on the same job simultaneously, how many minutes will it take all of them to complete it?
Options:
A)8
B)21
C)24
D)27
E)30
Rationale: C = A + B
D = 3C = 3(A+B) = 4B
Then B = 3A and C = 4A
The combined rate of the four machines is A + 3A + 4A + 12A = 20A
Machine A can complete the work in 420 minutes, so its rate is 1/420 of the work per minute.
The combined rate is 20/420 = 1/21 so the work will be completed in 21 minutes.
The answer is B.
Answer: B
Question: The difference between a number and its three fifth is 50. What is the number?
Options:
A)75
B)100
C)125
D)175
E)187
Rationale: Sol.
Let the numbers be x.
Then, x-3/5x = 50
⇔2/5x = 50⇔ x = (50x5/2) = 125.
Answer C
Answer: C
Question: If x = y+3+4.5x and y = x+18, what is the value of y/x ?
Options:
A)-6/5.
B)-7/20.
C)1/4.
D)-20/7.
E)1.5.
Rationale: (1) x = y + 3 + 4.5x
Substitute y for y = x + 18 (Eq. we are given)
x = x + 18 + 3 + 4.5x
Combine like terms
x = 5.5x + 21 --> -4.5x = 21 --> x = -14/3
(2) y = x + 18
Substitute x for x = -14/3
y = (-14/3) + 18 = 40/3
(3) x/y = ?
Substitute x and y we found above
y/x = (40/3) /(-14/3) = (40/3) * (-3/14) = -40/14 = -20/7
My answer: D
Answer: D
Question: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
Options:
A)5729
B)5760
C)5729
D)5720
E)5192
Rationale: 1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4 = 5760
Answer:B
Answer: B
Question: What will be the compound interest on a sum of Rs. 20,000 after 3 years at the rate of 12% p.a.?
Options:
A)s.10123.22
B)s.10823.20
C)s.10123.20
D)s. 8098.56
E)s.10123.28
Rationale: Explanation:
Amount = [20000 * (1 + 12/100)3]
= 20000 * 28/25 * 28/25 * 28/25 = Rs. 35123.20
C.I. = (35123.20 - 20000) = Rs. 8098.56
Answer:D
Answer: D
Question: A company has 600 employees, 40% of whom are employed Full time. If it hires 100 new employees, 15% of whom are employed part time, what will be the new percent of part time employees in total?
Options:
A)1 2/3 %
B)2 2/3 %
C)4 %
D)46.43 %
E)9 %
Rationale: Total employee = 600
Full time Empl = 600 * 40/100 =240
Part time Emp = 600 - 240 = 360
New part time empl = 100 * (15/100)
=15
Total new part time Emp = 15+360= 375
Old part time Emp = 360
Total Emp = 600 + 100 = 700
% of new part-time = (Total employee - new part time)*100 /total emp
= (700-375)*100/700
= 46.43 %
D
Answer: D
Question: A swimmer can swim in still water at 4 km/h. If the speed of the water current is 2 km/h, how many hours will the swimmer take to swim against the current for 5 km?
Options:
A)2.0
B)2.5
C)3.0
D)3.5
E)4.0
Rationale: The swimmer can swim against the current at a speed of 4-2 = 2 km/h.
The time it will take is 5/2 = 2.5 hours.
The answer is B.
Answer: B
Question: An anti aircraft gun can fire four shots at a time. If the probabilities of the first, second, third and the last shot hitting the enemy aircraft are 0.7, 0.6, 0.5 and 0.4, what is the probability that four shots aimed at an enemy aircraft will bring the aircraft down?
Options:
A)0.084
B)0.916
C)0.036
D)0.964
E)0.92
Rationale: Sum of probabilities of each shot= 0.7+0.3*0.6+0.3*0.4*0.5+0.3*0.4*0.5*0.4
=0.964
ANSWER:D
Answer: D
Question: The diameter of the driving wheel of a bus is 140 cm. How many revolution, per minute must the wheel make in order to keep a speed of 66 kmph ?
Options:
A)33
B)250
C)138
D)278
E)288
Rationale: Explanation:
Circumference = No.of revolutions * Distance covered
Distance to be covered in 1 min. = (66 X1000)/60 m = 1100 m.
Circumference of the wheel = 2 x (22/7) x 0.70 m = 4.4 m.
Number of revolutions per min. =(1100/4.4) = 250.
Answer: B) 250
Answer: B
Question: Jackson invested $600,000, dividing it all unequally between Account P and Account Q. At the end of the year, it turned out that Account P had earned 12% interest and Account Q had earned 25% interest. If Jackson earned a total of $60,000 in interest between the two accounts, which of the following is approximately the amount he put in account P?
Options:
A)$115,384
B)$120,000
C)$121,072
D)$124,129
E)$130,000
Rationale: x be the amount invested in account P
0.12*x +(600000-x)*0.25=60,000
15000/.13=x
x=1500000/13=11...=$124,129
hence answer is D
Answer: D
Question: To mail a package, the rate is u cents for the first pound and v cents for each additional pound, where u>v. Two packages weighing 3 pounds and 5 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
Options:
A)Combined, with a saving of u-v cents
B)Combined, with a saving of y-x cents
C)Combined, with a saving of x cents
D)Separately, with a saving of x-y cents
E)Separately, with a saving of y cents
Rationale: This means it costs x cent for the first pound in weight for example, 20 cents for the first pound.
It costs y cents for the every pound in weight above this, for example 10 cents for pound 2 and 10 cents for pound 3.
x is more than y. for example 20 cents vs. 10 cents
3 pounds: x+2y
5 pounds:x+4y
Total: 2x+6y
8 pounds: x+7y
So we are saving:
(2X+6y) - x+7y
= x-y cents
Combined is cheaper as we maximise y and minimize x.
Answer is:
1) Combined, with a saving of x-y cents
Answer: A
Question: Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 5 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
Options:
A)32 km
B)20 km
C)65 km
D)18 km
E)16 km
Rationale: Distance = Relative Speed * Time
= (5 + 3) * 4 =32 km
[ They are travelling in the opposite direction, relative speed
= sum of the speeds].
Answer: A
Answer: A
Question: A certain business produced x rakes each month form November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.60 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months form November through October?
Options:
A)0.40x
B)1.20x
C)1.40x
D)1.60x
E)3.20x
Rationale: because we have a total of 4X
Also from Mar- Oct the rakes will be deducted by 1/8 X
so
In Apr they pay for the storage 0.6 * 4X * 7/8
In May they pay for the storage 0.6 * 4X * 6/8
In Jun they pay for the storage 0.6 * 4X * 5/8
In Jul they pay for the storage 0.6 * 4X * 4/8
In Aug they pay for the storage 0.6 * 4X * 3/8
In Sep they pay for the storage 0.6 * 4X * 2/8
In Oct they pay for the storage 0.6 * 4X * 1/8
total = 0.1 * 4X * 1/8 * [ 1+2+3+4+5+6+7]
= 0.6 * X/2 * (28)
= 8.4X
(E)
Answer: E
Question: Set A contains all the even numbers between 6 and 50 inclusive. Set B contains all the even numbers between 106 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
Options:
A)2300
B)2550
C)5050
D)6275
E)11325
Rationale: Set A contains 6, 8, ... 50
Set B contains 102 , 104 , 106 ... 150
Number of terms in each set = 23
Difference between corresponding terms in set A and B = 100
Difference between Sum of set B and set A = 100*23 = 2300
Answer A
Answer: A
Question: A clothing store purchased a pair of pants for $90 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price. After some time a clothing store owner decided to decrease the selling price by 20 percent. What was the clothing store's gross profit on this sale?
Options:
A)$14
B)$5
C)$10
D)$6
E)$8
Rationale: Sale Price(SP) = 90 + Markup(MP)
--> Mp = SP-90
and given MP=SP/4 ( 25% is 1/4th)
so SP/4= SP-90
3SP/4= 90
SP=120
Now a discount of 20% is given so NEW SP is .8 *120 =96
Profit=96-90 =6.0$
Answer is D
Answer: D
Question: A = {0, 1, -3, 6, -8}
B = {-1, 2, -4, 7}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?
Options:
A)1/4
B)1/3
C)2/5
D)4/9
E)1/2
Rationale: For the product of 2 numbers to be positive either both of them must be positive or both of them must be negative:
P(positive, positive) = 2/5*2/4 = 4/20;
P(negative, negative) = 2/5*2/4 = 4/20.
P = 4/20 + 4/20 = 8/20 = 2/5.
Answer: C.
Answer: C
Question: If (1 / 3.718) = 0.2689, Then find the value of (1 / 0.0003718).
Options:
A)2689
B)2869
C)2968
D)2986
E)None of them
Rationale: (1 / 0.0003718 ) = ( 10000 / 3.718 ) = 10000 * (1 / 3.718) = 10000 * 0.2689 = 2689.
Answer is A.
Answer: A
Question: A picnic attracts 240 persons. There are 60 more men than women, and 60 more adults than children. How many men are at this picnic?
Options:
A)240
B)75
C)110
D)130
E)85
Rationale: Adult + Children = 240
Let, Children = y
then, Adult = y+60
i.e. y+(y+60) = 240
i.e. y = 90
i.e. Adult = 90+20 = 110
Adults include only Men and Women
i.e. Men + Women = 110
Let women, W = x
then Men, M = x+60
i.e. x+(x+60) = 2x+60 = 110
i.e. x = 25
i.e. Men, M = 25+60 = 85
Answer: Option E
Answer: E
Question: A certain debt will be paid in 52 installments from January 1 to December 31 of a certain year. Each of the first 22 payments is to be $410; each of the remaining payments is to be $65 more than each of the first 22 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year?
Options:
A)447.5
B)450
C)465
D)468
E)475
Rationale: Total number of installments = 52
Payment per installment for the first 22 installments = 410
Payment per installment for the remaining 30 installments = 410+65=475
Average = (22*410 + 30*475)/52 = 447.50
Answer A
Answer: A
Question: The length of a rectangle is reduced by 20%. By what % would the width have to be increased to maintainthe original area?
Options:
A)10%
B)21%
C)25%
D)40%
E)45%
Rationale: Sol. Required change = (20*100)/(100-20)=25%
C
Answer: C
Question: A bag contains 5 red, 6 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
Options:
A)1/13
B)2/23
C)5/39
D)4/27
E)3/23
Rationale: P(Both are red),
5C213C2=6C213C2
=10/78=5/39
C
Answer: C
Question: The batting average of a particular batsman is 59 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score.
Options:
A)156
B)208
C)210
D)223
E)229
Rationale: Explanation:
Total runs scored by the batsman = 59*46 = 2714 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2714 – 2552 = 162 runs.
Let the highest score be x, hence the lowest score = x – 150
x + (x - 150) = 162
2x = 312
x = 156 runs
ANSWER A
Answer: A
Question: How many two digit numbers are there such that the product of their digits after reducing it to the smallest form is a prime number? for example if we take 98 then 9*8=72, 72=7*2=14, 14=1*4=4. Consider only 4 prime no.s (2,3,5,7)
Options:
A)16
B)17
C)18
D)19
E)20
Rationale: we know prime no. are 2 ,3 , 5, 7
mulply by 1 is prime no
2 = 21(2*1)=73(7*3)
2 = 21 (2*1)=37(3*7)
2= 12(1*2)=43(4*3)or34(3*4)
or26(2*6)or62(6*2)
.
.
.similarly for all prime no then u will got it....
12,13,15,17,21,26,31,34,35,37,43,51,53,57,62,71,73,75
ans is 18
ANSWER:C
Answer: C
Question: When positive integer N is divided by positive integer J, the remainder is 12. If N/J = 134.08, what is value of J?
Options:
A)22
B)56
C)78
D)112
E)150
Rationale: 1) We know that
decimal part of decimal quotient ={remainder/divisor}
So 0.08, the decimal part of the decimal quotient, must equal the remainder, 12, divided by the divisor J.
0.08 = 12/J
0.08*J = 12
J = 12/0.08 = 1200/8 = 300/2 = 150
So J = 150, answer = E.
Answer: E
Question: A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 90.Find the number of notes of Rs.50 denomination.
Options:
A)15
B)21
C)17
D)57
E)77
Rationale: Total Money = Rs. 10350.
Let 50 rupees note was X.
Then 500 rupees note = 90 - X
Now,
50*X + 500 * (90 - X) = 10350
50X + 45000 - 500X = 10350
- 450X = - 34650
X = 77.
No. of 50 rupees note = 77.
Answer: Option E
Answer: E
Question: What is the difference between the C.I. on Rs. 5000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?
Options:
A)Rs.2.04
B)Rs.2.08
C)Rs.2.02
D)Rs.2.83
E)Rs.2.42
Rationale: C.I. when interest is compounded yearly
= [5000 * (1 + 4/100) * (1 + (1/2 * 4)/100]
= 5000 * 26/25 * 51/50 = Rs. 5304
C.I. when interest is compounded half-yearly
= [5000 * (1 + 2/100)2]
= (5000 * 51/50 * 51/50 * 51/50)
= Rs. 5306.04 Difference
= (5306.04 - 5304)
= Rs.2.04.
Answer: A
Answer: A
Question: A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?
Options:
A)3xr/2
B)3x/200r
C)3r/200x
D)3xr/200
E)xr/600
Rationale: r/100 dollars per person per mile
one person going x miles will be charged rx/100
50% discount = rx/200
3 such people = 3rx/200 ;
ANSWER:D
Answer: D