divelab/Sys2Bench huggingface dataset:
Question: A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
Options:
A)4:7
B)4:9
C)4:3
D)4:6
E)4:2
Rationale: 12:9
= 4:3
Answer:C
Answer: C
Question: Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Sunday, what was the expected day when both the brothers were to return home and when did Rohit Return?
Options:
A)Thursday, Monday
B)Sunday, Thursday
C)Wednesday, Sunday
D)Monday, Friday
E)none
Rationale: Rajat returned on Sunday -i.e. 3 days earlier
so actual day to return home is Wednesday.
Rohit returned after days so Sunday
ANSWER:C
Answer: C
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Options:
A)187
B)180
C)289
D)216
E)279
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer:B
Answer: B
Question: Two pipes A,B can fill a tank in 24 min. and 32 min. respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min.?
Options:
A)8 min
B)9 min
C)7 min
D)6 min
E)5 min
Rationale: work done by A => 18/24
work done by B => x/32
18/24 + x/32 = 1
3/4 + x/32=1
24+x=32 => x=8
ANSWER:A
Answer: A
Question: Which of the following integers is NOT a divisor of x if x = (21)(3^7) – (7)?
Options:
A)2
B)4
C)7
D)9
E)10
Rationale: (21)(3^7) is divisible by 3 but 7 is not divisible by 3.
Therefore (21)(3^7) - 7 is not divisible by 3 and thus not divisible by 9.
The answer is D.
Answer: D
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head. The following day the rest were sold at a price equal to 40% less than the price each head sold for on the day before. What was the total gross profit on this shipment.
Options:
A)$100
B)b $115
C)c $125
D)d $50
E)e $135
Rationale: Purchase cost = 600/1500= $ 0.4
25% above the cost per head = (125/100)*0.4= $ 0.5
2/3 of the heads were sold means 2/3*1500 =1000 ,Selling amount for 1000 cabbage = 1000 * 0.5 = $ 500
Remaining were sold at a price equal to 40% less than the price each head sold for on the day before i.e , (60/100)*0.5 = $ 0.3
Hence selling cost for the remaining cabbage = 500 * 0.3 = $ 150
Total selling cost = 500 + 150 = $ 650
Gross profit = $ 650 - $ 600 = $ 50
Hence Answer is D.
Answer: D
Question: A machine puts c caps on bottles in m minutes. How many T hours will it take to put caps on b bottles?
Options:
A)60bm/c
B)T=bm/60c
C)bc/60m
D)60b/cm
E)b/60cm
Rationale: The machine puts c caps in m minutes or c caps in m/60 hours.
Rate = c/m/60 = 60c/m.
To put b caps the machine will take:-
Time = Work/Rate
T = b/60c/m = bm/60c
Answer is B.
Answer: B
Question: Raja was born 4 years after his father's marriage. His mother is 4 years younger than his father but 20 years older than Raja who is 20 years old. At what age did the father get married ?
Options:
A)30 years
B)25 years
C)20 years
D)22 years
E)21 years
Rationale: Explanation:
Raja's present age = 20 years.
His mother's present age = (20 + 20) years = 40 years.
His father's present age = (40 + 4) years = 44 years.
His father's age at the time of Raja's birth = (44 - 20) years = 24 years.
Therefore Raja's father's age at the time of marriage = (24 - 4) years = 20 years.
Answer: C
Answer: C
Question: Two integers are in the ratio of 1 to 3. If 10 is added to the smaller number, the ratio becomes 1 to 1. Find the larger integer.
Options:
A)6
B)9
C)10
D)12
E)15
Rationale: One option is to set up the equations and solve:
If the ratio of two integers x and y is 1 to 3, then 3x=y, where x is the smaller integer.
If adding 10 to the smaller integer makes the ratio 1 to 1, then x+10=y.
Substituting y=3x into the second equation yields x+10=3x.
So, x=5 (smaller integer) and, y=3x=15 (larger integer) so E is the correct answer.
Another option is to TEST the answer choices.
A) the larger number is 6
Given: the two integers are in the ratio of 1 to 3
So, the smaller number must be 2
If 10 is added to the smaller number, the ratio becomes 1 to 1
If we add 10 to the smaller number (2), we get 12.
So, the new ratio is 12 to 6 which is the same as 2 to 1.
No good. We want a resulting ratio of 1 to 1
ELIMINATE A
B) the larger number is 9
Given: the two integers are in the ratio of 1 to 3
So, the smaller number must be 3
If 10 is added to the smaller number, the ratio becomes 1 to 1
If we add 10 to the smaller number (3), we get 13
So, the new ratio is 13 to 9.
No good. We want a resulting ratio of 1 to 1
ELIMINATE B
C) the larger number is 10
Given: the two integers are in the ratio of 1 to 3
So, the smaller number must be 3.33 (which is not an integer)
Since both numbers are integers, the larger number cannot be 10.
ELIMINATE C
D) the larger number is 12
Given: the two integers are in the ratio of 1 to 3
So, the smaller number must be 4
If 10 is added to the smaller number, the ratio becomes 1 to 1
If we add 10 to the smaller number (4), we get 14
So, the new ratio is 14 to 12 which is 7 to 6.
No good. We want a resulting ratio of 1 to 1
ELIMINATE D
E) the larger number is 15
Given: the two integers are in the ratio of 1 to 3
So, the smaller number must be 5
If 10 is added to the smaller number, the ratio becomes 1 to 1
If we add 10 to the smaller number (5), we get 15
So, the new ratio is 15 to 15. This is the same as the ratio of 1 to 1
Therefore E is the only correct choice.
Answer: E
Question: 95% of the house of a city is 7600. The total house of the city is?
Options:
A)7500
B)8250
C)10000
D)7750
E)8000
Rationale: X * (95/100) = 7600
X = 80 * 100
X = 8000
Answer: E
Answer: E
Question: When I was married 10 years ago, my wife was the sixth member in the family. Today, my father died,and a baby was born to me. The average age in my family today is what it was when I was married.How old was my father when he died?
Options:
A)50 years
B)60 years
C)70 years
D)80 years
E)Indeterminate
Rationale: If x was average age 10 years ago, then total age 10 years ago = 10x.
Total age of 6 persons before death of father = 10x+60
Total age of 6 persons ( excluding father and adding son of zero age) after death of father = 60x as average of family is x again.
Hence age of father at time of death = x+60-x = 60 years
ANSWER:B
Answer: B
Question: A boat can travel with a speed of 25km/hr in still water. If the speed of the stream is 5km/hr, find the time taken by the boat to go 120km downstream.
Options:
A)1 hr
B)2 hrs
C)3 hrs
D)4 hrs
E)5 hrs
Rationale: Speed downstream = (25 + 5) km/hr = 30 km/hr.
Time taken to travel 120 km downstream = 120/30 hrs = 4 hrs.
Answer : D
Answer: D
Question: The ratio of male to female in a class is 3:4. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one third of the males and two-third of the females in the class?
Options:
A)a)160 degree
B)b) 168 degree
C)c)264 degree
D)d)192 degree
E)e)204 degree
Rationale: let the common ratio be x.. so M=3x and F=4x and Total=7x
1/3 of M= 3x/3 and 2/3 of F= 8x/3
Total preferring that carrer = x+8x/3=11x/3
Now 5x= 360, so x=360/5=72..
so x*8/3= 72*11/3=192
C
Answer: C
Question: A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 32 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture?
Options:
A)2:5
B)5:14
C)3:5
D)4:7
E)14:5
Rationale: The first drink has 6 oz, which are 2 oz rum and 4 oz coke. The second drink is 32 oz, which are 8 oz rum and 24 oz coke. The resulting mixture is then 38 oz (10 oz rum and 28 oz coke). Overall, this is 10 oz rum: 28 oz coke, which is a 5:14 ratio.
Answer is B
Answer: B
Question: If x, y, and z are positive integers and 3x = 7y = 5z, then the least possible value of x + y + z is
Options:
A)15
B)25
C)71
D)35
E)45
Rationale: given 3x=7y=5z
x+y+z in terms of x
= x+(3x/7)+(3x/5) = 71x/35
now checking with each of the answers and see which value gives a minimum integer value.
A x = 35/71*15 , not an integer
B,D,E can be ruled out similarly.
C is minimum value as x = 71*35/71 = 35
Answer is C
Answer: C
Question: HCF and LCM two numbers are 14 and 396 respectively. If one of the numbers is 36, then the other number is?
Options:
A)36
B)66
C)154
D)264
E)364
Rationale: 14 * 396 = 36 * x
x = 154
ANSWER:C
Answer: C
Question: 99,995^2 - 5^2 =
Options:
A)10^10 - 2
B)(10^5 – 2)^2
C)10^4(10^5 – 2)
D)10^5(10^5 – 10)
E)10^5(10^5 – 2)
Rationale: (99,995)^2 - (5)^2 = (100,000 -5)^2 - (5)^2 = (100,000)^2 - 2*5*100,000 + 5^2-5^2=(10^5)^2 - 10*(10^5) = 10^10 - 10*(10^5)=10^5(10^5 - 10) Answer D
Answer: D
Question: Of the families in City X in 1994, 40 percent owned a personal computer. The number of families in City X owning a computer in 1998 was 30 percent greater than it was in 1994, and the total number of families in City X was 4 percent greater in 1998 than it was in 1994. what percent of the families in City X owned a personal computer in 1998?
Options:
A)50%
B)52%
C)56%
D)70%
E)74%
Rationale: Say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 40
Number of families owning computer in 1998 = 40 * 130/100 = 52
Number of families in 1998 = 104
The percentage = 52/104 * 100 = 50%.
ANSWER:A
Answer: A
Question: If 2805 / 2.55 = 1100, then 280.5 / 25.5 is equal to ?
Options:
A)1.01
B)1.1
C)0.11
D)11
E)None
Rationale: Answer
Given expression 280.5 / 25.5 = 2805 / 255
= 2805 / (2.55 x 100)
= 1100 / 100
=11
Correct Option: D
Answer: D
Question: In a series of consecutive odd numbers, 27 is the eighth smallest number and 25 is the ninth largest number. What is the range of the series?
Options:
A) 32
B) 30
C) 28
D) 16
E) 14
Rationale: Imp:All are consecutive odd numbers.
27 is the 8th smallest ,there are 7 numbers smaller then 27 ,smallest number :27-14=13
25 is the 10th largest ,so there are 8 numbers larger then 25, largest number:25+16=41
Range:41-13=28
Ans : C
Answer: C
Question: If q and t are positive integers, qt + q + t cannot be
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Let qt + t +q = x
Add 1 on both sides:
qt + t + q + 1 = x + 1
tq + 1) + q + 1 = x + 1
(q + 1)(t + 1) = x + 1
Minimum value of (q + 1) = 2
Minimum value of (t + 1) = 2
Hence x + 1 cannot be prime
Substitute x from the given options: 6 + 1 = 7 --> prime --> qt + t + s cannot be 6
Answer: B
Answer: B
Question: A basketball player is shooting hoops. He shoots a free throw, a high school 3-pointer, and then a professional 3-pointer. The probability that he makes the free throw is 4/5, the probability that he makes the high school 3-pointer is 1/2, and the probability that he makes the professional 3-pointer is 1/3. What is the probability that he makes at least one of the three shots?
Options:
A)14/15
B)15/16
C)17/18
D)9/10
E)5/6
Rationale: The probability that he makes at least one of the three shots = 1 - (the probability that he misses all of the shots)
The probability that he misses all shots = (prob that he misses free throw)*(prob that he misses 3-pointer)*(prob that he misses the professional 3-pointer)
Prob that he misses the free throw = 1 - 4/5 = 1/5; Prob that he misses the 3-pointer = 1 - 1/2 = 1/2; Prob that he misses the professional 3-pointer = 1 - 1/3 = 2/3
Thus the probability that he misses all shots = (1/5)*(1/2)*(2/3) = 1/15
Answer: 1 - 1/15 = 14/15
A
Answer: A
Question: A man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is
Options:
A)16
B)14
C)15
D)18
E)20
Rationale: Explanation:
Let the son's present age be x years. Then, man's present age = (x + 20) years
=> (x + 20) + 2 = 2(x + 2)
=> x + 22 = 2x + 4
So, x = 18. Answer: D
Answer: D
Question: The compound ratio of 2/3, 6/7, 1/3 and 3/8 is given by?
Options:
A)7/98
B)1/48
C)1/98
D)1/96
E)3/42
Rationale: 2/3 * 6/7 * 1/3 * 3/8 = 36/504 = 3/42
ANSWER:E
Answer: E
Question: The average age of 6 men increases by 3 years when two women are included in place of two men of ages 24 and 26 years. Find the average age of the women?
Options:
A)37
B)26
C)34
D)18
E)11
Rationale: Explanation:
24 + 26 + 6 * 3 = 68/2 = 34
Answer: C
Answer: C
Question: A factory produces 8000 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
Options:
A)4436 toys
B)5487 toys
C)2000 toys
D)2354 toys
E)1375 toys
Rationale: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4.
8000 /4 = 2000 toys
correct answer C
Answer: C
Question: There are 760 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?
Options:
A)320
B)345
C)425
D)475
E)400
Rationale: In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 760. Hence
3x + 5x = 760
Solve for x
8x = 760
x = 95
Number of boys
3x = 3 × 95 = 285
Number of girls
5x = 5 × 95 = 475
D
Answer: D
Question: a boatman selling a boat along river flow.if he sell boat in steal water at 3m/sec and flow of river is 2m/sec.how much time he will take to sell 100m.
Options:
A)30
B)10
C)15
D)20
E)25
Rationale: net speed = 3+2=5 m/sec
distance = 100m
time=100/5=20sec
answer D
Answer: D
Question: If a and b are multiples of 9 then which are all the multiples of 9
1) a*b
2) a/b
3) a+b
4) a-b
5) a^b
Options:
A)1,2,5
B)all of these
C)1,3,4,5
D)2,3,4,5
E)1,3
Rationale: a*b a^b a+b a-b are multiples of 6 except a/b
ANSWER:C
Answer: C
Question: Mark has a rectangular driveway with a line painted diagonally across. The length of the driveway is 6 feet longer than its width. If the total area of the driveway is 40 square feet, what is the length of the painted line (in feet)?
Options:
A)Between 9 and 10
B)Between 10 and 11
C)Between 11 and 12
D)Between 12 and 13
E)Between 13 and 14
Rationale: To solve this, we first need to set up an equation for the area of the room. If x is the width, then we have
x(x + 6) = 40. By putting the equation in standard form, we get x^2+6x-40=0. By using the quadratic formula, we get roots of 4 and -10. We know that x is the width, and x+6 is the length, so by using the roots, we get 4 as the width (x), and 10 as the length (x+5).
Once we have this, we can use the Pythagorean Theorem to solve for the diagonal. Plugging in the length and width, we will get d^2=4^2+10^2
=16+100
=116
The square root of 97 is more than 10, since 10^2 = 100. Going up a number, we can compute 11^2 = 121 >116. Therefore, the length of the diagonal must be between 10 and 11.
The correct answer is B.
Answer: B
Question: Which greatest possible length can be used to measure exactly 15 meter 20 cm, 12 meter 20 cm and 14 meter 20 cm
Options:
A)20cm
B)25cm
C)24cm
D)55cm
E)30cm
Rationale: Explanation:
Convert first all terms into cm.
i.e. 1520 cm, 1220cm, 1420cm.
Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 20.
Option A
Answer: A
Question: The sum of five numbers is 100. The average of the first two numbers is 10 and the third number is 30. Find the average of the two numbers?
Options:
A)25
B)20
C)23
D)22
E)30
Rationale: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 100
(P + Q)/2 = 10 and R = 30
P + Q = 20 and R = 30
P + Q + R = 50
S + T = 100 - (P + Q + R) = 50
Average of the last two numbers
= (S + T)/2 = 25
Answer:A
Answer: A
Question: Mira is making telescopes, each consisting of 2 lenses, 1 tube, and 1 eyepiece. Lenses can be purchased only in packs of 50, tubes only in packs of 10, and eyepieces only in packs of 30. However, half of the lenses in each pack are not usable for telescopes. If all parts are used only for the telescopes what is the minimum number of lenses Mira must purchase to make a set of telescopes with no leftover components other than the unusable lenses?
Options:
A)75
B)150
C)300
D)500
E)2400
Rationale: I'd use backsolving for this question.
Check E:
2400 lenses = 1200 usable lenses = 600 tubes = 600 eyepieces. We CAN buy 600 tubes and 600 eyepieces, so that not to have leftovers.
Answer: E.
Answer: E
Question: A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage?
Options:
A)88%
B)50%
C)87%
D)66%
E)54%
Rationale: L.C.M of 15 and 12 = 60
CP of 60 articles = Rs. 100 (25 * 4)
SP of 60 articles = Rs. 150 (30 * 5)
Profit percentage = (150 - 100)/100 * 100 = 50%
Answer: B
Answer: B
Question: A FIVE DIGIT NUMBER DIVISIBLE BY 3 IS TO BE FORMED USING THE DIGITS 0, 1, 2, 3, 4 and 5 WITHOUT REPETITIONS. THAT TOTAL NO OF WAYS IT CAN BE DONE IS?
Options:
A)122
B)210
C)216
D)217
E)220
Rationale: First step:
We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.
We have six digits: 0,1,2,3,4,5. Their sum=15.
For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0=(1,2,3,4,5) and 15-3=(0,1,2,4,5). Meaning that no other 5 from given six will total the number divisible by 3.
Second step:
We have two set of numbers:
1,2,3,4,5 and 0,1,2,4,5. How many 5 digit numbers can be formed using this two sets:
1,2,3,4,5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.
0,1,2,4,5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=96
120+96=216
Answer: C.
Answer: C
Question: A grocer has a sale of Rs. 2500, Rs. 4000, Rs. 3540 for 3 consecutive months. How much sale must he have in the fourth month so that he gets an average sale of Rs. 2890?
Options:
A)Rs.3500
B)Rs. 1520
C)Rs. 4996
D)Rs. 4000
E)Rs. 900
Rationale: Total sale for 5 months = Rs. ( 2500 + 4000 + 3540) = Rs. 10040.
Required sale = Rs. [ (2890 x 4) -10040 ]
= Rs. (11560 - 10040)
= Rs. 1520.
B)
Answer: B
Question: A man reaches his office 20 min late, if he walks from his home at 3 km per hour and reaches 30 min early if he walks 4 km per hour. How far is his office from his house ?
Options:
A)50 km
B)80 km
C)20 km
D)10 km
E)30 km
Rationale: Explanation:
Let distance = x km.
Time taken at 3 kmph : dist/speed = x/3 = 20 min late.
time taken at 4 kmph : x/4 = 30 min earlier
difference between time taken : 30-(-20) = 50 mins = 50/60 hours.
x/3- x/4 = 50/60
x/12 = 5/6
x = 10 km.
Answer: D
Answer: D
Question: Sarah operated her lemonade stand Monday through Friday over a two week period and made a total profit of 350 dollars. On hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days. Each cup she sold had a total cost of 75 cents and Sarah did not incur any other costs. If every day she sold exactly 32 cups and 4 of the days were hot, then what was the price of 1 cup on a hot day?
Options:
A)$ 1.50
B)$ 1.88
C)$ 2.09
D)$ 2.50
E)$ 3.25
Rationale: 6 regular days --> sales = 6*32*x = 192x;
4 hot days --> sales = 4*32*(1.25x) = 160x;
Total sales = 192x+160x = 352x.
Total cost = 10*32*0.75 = 240.
Profit = 352x - 240 = 350 --> x=1.676.
1.25x=~2.09.
Answer: C.
Answer: C
Question: A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.10 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?
Options:
A)1788
B)1200
C)2789
D)1776
E)1999
Rationale: l * 30 = 1200 è l = 40
40 + 30 + 50 = 120
120 * 10 = 1200
Answer: B
Answer: B
Question: A reduction of 40% in the price of bananas would enable a man to obtain 65 more for Rs.40, what is reduced price per dozen?
Options:
A)1.95
B)2.95
C)4.95
D)3.95
E)5.95
Rationale: 40*(40/100) = 16 --- 65
? --- 12 => Rs.2.95
Answer: B
Answer: B
Question: A train 120 m in length crosses a telegraph post in 6 seconds. The speed of the train is?
Options:
A)72 kmph
B)88 kmph
C)54 kmph
D)18 kmph
E)19 kmph
Rationale: S = 120/6 * 18/5
= 72 kmph
Answer: A
Answer: A
Question: If (1 – 1.25)N = 5, then N =
Options:
A) −20
B) −140
C) −4
D) 4
E) 400
Rationale: (1 – 1.25)N = 5
Simplify to get: -0.25N = 5
Rewrite as (-1/4)N = 5
Multiply both sides by -4 to get: N = -20
Answer: A
Answer: A
Question: A and B together can complete work in 5 days. A alone starts working and leaves it after working for 3 days completing only half of the work. In how many days it can be completed if the remaining job is undertaken by B?
Options:
A)4
B)8
C)15
D)6
E)7
Rationale: Explanation:
(A+B) one day work =1/5
now A does half of the work in 3 days so A can complete the whole work in 6 days
A’s one day work =1/6
B’s one day work=1/5 - 1/6= 1/30
B alone can complete the work in 30 days so half of the work in 15 days
Answer: Option C
Answer: C
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
Options:
A)337
B)278
C)221
D)860
E)121
Rationale: Explanation:
CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer:D
Answer: D
Question: Suppose 7 students are staying in a hall in a hostel and they are allotted 7 beds. Among them, Parvin does not want a bed next to Anju because Anju snores. Then, in how many ways can you allot the beds?
Options:
A)600
B)620
C)670
D)690
E)700
Rationale: Suppose Anju is allotted bed number 1.
Then, Parvin cannot be allotted bed number 2.
So Parvin can be allotted a bed in 5 ways.
After allotting a bed to Parvin, the remaining 5 students can be allotted beds in 5! ways.
So, in this case the beds can be allotted in 5×5!=6005×5!=600 ways.
Option is A
Answer: A
Question: A man is 22 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
Options:
A)23 years
B)22 years
C)21 years
D)20 years
E)19 years
Rationale: Let present age of the son =x years
Then, present age the man =(x+22) years
Given that, in 2 years, man's age will be twice the age of his son
â‡’(x+22)+2=2(x+2)
â‡’x=20
ANSWER:D
Answer: D
Question: Which of the following is a prime number ?
Options:
A)2
B)1
C)5
D)4
E)3
Rationale: 2 is a prime number. A prime number is a natural number greater than 1 which has no positive divisors other than 1 and itself. Hence the primer numbers are 2,3,5,7,11,13,17,...
Answer is A.
Answer: A
Question: Find the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.
Options:
A)121
B)124
C)127
D)122
E)129
Rationale: Required number = H.C.F. of (1657 - 6) and (2037 - 5) = H.C.F. of 1651 and 2032
_______
1651 ) 2032 ( 1 1651
1651_______
381 ) 1651 ( 4
1524_________
127 ) 381 ( 3
381
0
Required number = 127.
Answer is C.
Answer: C
Question: Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 30% and 20% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
Options:
A)18%
B)20%
C)21%
D)23%
E)Cannot be determined
Rationale: Answer: D.
Answer: D
Question: If a and b are two-digit integers such that a > 20 and b<60, which of the following is closest to the maximum possible value of ab ?
Options:
A) 700
B) 2,800
C) 5,841
D) 7,000
E) 28,000
Rationale: To get the maximum possible value of ab, we need maximize the value of both a and b
max a can be = 99 (given a is a two-digit integer > 20)
max b can be = 59 (given b is a two-digit integer < 60)
xy = 99*59 = 5841
Answer (C)
Answer: C