divelab/Sys2Bench huggingface dataset:
Question: A certain company reported that the revenue on sales increased 50 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005?
Options:
A) 20 %
B) 40 %
C) 35 %
D) 32 %
E) 29 %
Rationale: Assume the revenue in 2000 to be 100. Then in 2003 it would be 150 and and in 2005 180, so from 2003 to 2005 it increased by (180-150)/150=30/150=~20%.
Answer: A
Answer: A
Question: A, B and C started a shop by investing Rs. 4,000, Rs. 12,000 and Rs. 8,000 respectively. At the end of the year, the profits were distributed among them. If Câ€™s share of profit be Rs. 1,000, then the total profit was :
Options:
A)3,000
B)60,000
C)80,000
D)120,000
E)None
Rationale: Sol.
A : B : C = 4000 : 12000 : 8000 = 1: 3 : 2. so, Câ€™s share : Total Profit = 2 : 6
Let the total profit be Rs. x. Then, 2/6 = 1000/x or x
= 1000 * 6/ 2 = 3000.
Answer A
Answer: A
Question: If 3x+y=40, 2x-y=20, for integers of x and y, 2y^2=?
Options:
A)2
B)4
C)0
D)10
E)32
Rationale: 3x+y = 40
2x-y = 20
5x = 60
x = 12
y = 4
2y^2 = 2*16=32
Answer is E
Answer: E
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
Options:
A)288
B)267
C)108
D)285
E)171
Rationale: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 20)/100] = Rs. 285.
Answer: D
Answer: D
Question: If x and y are numbers such that (x+3)(y-3)=0, what is the smallest possible value of x^2 + y^2
Options:
A)0
B)3
C)6
D)9
E)12
Rationale: From (x+3)(y-3)=0 it follows that either x=-3 or y=3. Thus either x^2=9 or y^2=9.
Now, if x^2=9, then the least value of y^2 is 0, so the least value of x^2 + y^2 = 9 + 0 = 9.
Similarly if y^2=9, then the least value of x^2 is 0, so the least value of x^2 + y^2 = 0 + 9 = 9.
Answer: D.
Answer: D
Question: The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 3:5:7, the price of the cheapest item is?
Options:
A)2379
B)2889
C)9288
D)9000
E)28311
Rationale: Let their prices be 3x, 5x and 7x.
Then, 3x + 5x + 7x = (15000 * 3) or x = 3000.
Cost of cheapest item = 3x = Rs. 9000.
Answer: D
Answer: D
Question: Audrey has a bag of apples that weighs 200g. If she uses 62g of apples from the bag to make pies, what percent of her bag did she use?
Options:
A)50%
B)29%
C)36%
D)31%
E)22%
Rationale: Explanation :
Original weight of the bag: 200
Required percentage = (62/200) Ã— 100 = 31%
Answer : Option D
Answer: D
Question: If Jake loses 8 pounds, he will weigh twice as much as his sister Kendra. Together they now weigh 281 pounds. What is Jake’s present weight, in pounds?
Options:
A)125
B)135
C)140
D)165
E)190
Rationale: J + K = 281 and so K = 281 - J
J - 8 = 2K
J - 8 = 2(281-J)
3J = 570
J = 190
The answer is E.
Answer: E
Question: There are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
Options:
A)Rs. 30
B)Rs. 34
C)Rs. 42
D)Rs. 48
E)Rs. 50
Rationale: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1
or, 35x + 42 = 42x – 42
or, x = 12
Thus the original expenditure of the mess = 35 x 12 = Rs. 42
C
Answer: C
Question: How many positive integers less than 247 are multiple of 4 but NOT multiples of 6?
Options:
A)20
B)41
C)42
D)53
E)64
Rationale: From here, it might be easier to go up in bounds of 60, so we know that 61-120 gives 10 more numbers. 121-180 and 181-240 as well. This brings us up to 240 with 40 numbers. A cursory glance at the answer choices should confirm that it must be 41, as all the other choices are very far away. The numbers 244 will come and complete the list that’s (naughty or nice) under 250. Answer choice B is correct here.
Answer: B
Question: How many different sections of 4 books can be made from 10 different books if two particular books are never selected.
Options:
A)80
B)40
C)60
D)50
E)70
Rationale: If two particular books are never selected. This means 4 books are selected out of the remaining 8 books. Required number of ways =8C4 = 8!/4!4! =70. Answer : E
Answer: E
Question: The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 20 runs. Find his average in all the 30 matches?
Options:
A)31
B)46
C)88
D)33.33
E)12
Rationale: Total score of the batsman in 20 matches = 800.
Total score of the batsman in the next 10 matches = 200.
Total score of the batsman in the 30 matches = 1000.
Average score of the batsman = 1000/30 = 33.33
Answer:D
Answer: D
Question: A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,060 ?
Options:
A)$12
B)$14
C)$10.8
D)$17
E)$18
Rationale: I solved it as follows:
10+2(x) = 100 -5(x)
x= 12
Equation should be (10+$2*x)(100-5x)=1,060, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,060 --> (5+x)(20-x)=6 --> x=0.4 or x=14.6 --> price=10+$2*0.4=$10.8 or price=10+$2*14.6=$39.2.
Answer: C.
Answer: C
Question: (1/4 + 1/4 ÷ 5/4) / (1/4 x 1/4 + 2 1/4) = ?
Options:
A)16/25
B)32/185
C)36/185
D)None of these
E)Cannot be determined
Rationale: Answer
Given expression = (1/4 + 1/4 x 4/5) / (1/16 + 9/4)
= (1/4 + 1/5) / (37/16)
= 9/20 x 16/37
= 36/185
Correct Option: C
Answer: C
Question: In what ratio must tea at Rs.65 per Kg be mixed with tea at Rs.70 per Kg so that the mixture must be worth Rs.6 per Kg?
Options:
A)1 : 1
B)3 : 2
C)4 : 3
D)5 : 3
E)None
Rationale: Required ratio = 500 : 500 = 1 : 1
Answer A
Answer: A
Question: A certain number when divided by 39 leaves a remainder 16, what is the remainder when the same number is divided by 13?
Options:
A)7
B)8
C)9
D)6
E)3
Rationale: Explanation:
39 + 16 = 55/13 = 3 (Remainder)
Answer: E
Answer: E
Question: A newly-wed couple is using a website to design an eBook Wedding Album to distribute to their friends and families. The template they have chosen has places for 3 large photos and 18 smaller photos. The couple has 6 large photos they could use for those three slots, and 21 smaller photos they could use for those 18 slots. Given these choices, how many different possible albums could they create?
Options:
A)3,150
B)4,200
C)5,040
D)20,520
E)26,600
Rationale: MAGOOSHOFFICIAL SOLUTION:
For the large photos, we need 6C3, which we calculated in the article:
6C3 = 20
For the smaller photos, we need 21C18, which by symmetry must equal 21C3, and we have a formula for that. In fact, in the article above, we already calculated that 21C3 = 1330.
Now, by the FCP, we just multiply these: total number of possible albums = 20*1330 = 26600.
Answer = E
Answer: E
Question: A and B started business in partnership investing Rs. 20,000 and Rs. 18,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
Options:
A)A)7500
B)B)7389
C)C)7379
D)D)8490.57
E)E)7637
Rationale: A:B:C = (20000 * 24) : (18000 * 24) : (20000 * 18) = 20:18:15
B's share = 25000 * 18/53 = Rs.8490.56
Answer: D
Answer: D
Question: A bag contains 3 red, 2 yellow and 4 green balls. 3 balls are drawn randomly. What is the probability that the balls drawn contain balls of different colours?
Options:
A)2/7
B)3/5
C)3/11
D)1/4
E)7/16
Rationale: Total number of balls = 3+2+4 = 9
n(S) = 9C3 = 84
n(E) = 3C1 * 2C1 * 4C1 = 3*2* 4 = 24
Probability = 24/84 = 2/7
Answer is A
Answer: A
Question: If 4x = 8y = 12z, then what is a possible sum of positive integers x, y, and z?
Options:
A)52
B)58
C)84
D)122
E)180
Rationale: 4x = 8y = 12z
x = 2y = 3z
3(2*3) = 2(3*1) = 3(1*2)
Addition = 18+6+6 = 30
Answer would be multiple of 30 which is 180
Answer :E
Answer: E
Question: In a 1000 m race, A beats B by 80 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
Options:
A)145 m
B)172 m
C)268 m
D)129 m
E)218 m
Rationale: By the time A covers 1000 m, B covers (1000 - 80) = 920 m.
By the time B covers 1000 m, C covers (1000 - 100) = 900 m.
So, the ratio of speeds of A and C =
1000/920 * 1000/900 = 1000/828 So, by the time A covers 1000 m, C covers 828 m.
So in 1000 m race A beats C by 1000 - 828 = 172 m.
Answer:B
Answer: B
Question: 5.02 can be expressed in terms of percentage as
Options:
A)5.02%
B)50.2%
C)209%
D)502%
E)None of these
Rationale: Explanation:
While calculation in terms of percentage we need to multiply by 100, so
5.02 * 100 = 502
Answer: Option D
Answer: D
Question: What is the present worth of Rs. 165 due in 2 years at 5% simple interest per annum?
Options:
A)288
B)266
C)120
D)150
E)6123
Rationale: Let the present worth be Rs. x. Then,
S.I. = (165 - x)
(x * 5 * 2) / 100 = (165 - x)
10x = 16500 - 100x
110x = 16500 => x = 150.
Answer: D
Answer: D
Question: The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 31 inclusive.
Options:
A)220
B)364
C)410
D)424
E)450
Rationale: We're dealing with a sequence of CONSECUTIVE ODD INTEGERS: 13 to 31, inclusive. We're asked for the SUM of this group.
1) Start with the sum of the smallest and the biggest: 13 + 31 = 44
2) Now look at the 'next smallest' and the 'next biggest': 15 + 29 = 44
Now we have proof that there is no middle term. We have 5 bunches of 44
5(44) = 220
A
Answer: A
Question: A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 38. Find the profit percentage?
Options:
A)80%
B)90%
C)59%
D)40%
E)53%
Rationale: L.C.M of 15 and 12
= 60
CP of 60 articles
= Rs. 100 (25 * 4)
SP of 60 articles
= Rs. 190 (30 * 5)
Profit percentage
= (190 - 100)/100 * 100 = 90%
Answer: B
Answer: B
Question: A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:
Options:
A)120 kmph
B)140 kmph
C)220 kmph
D)320 kmph
E)330 kmph
Rationale: Let speed of the car be x kmph.
Then, speed of the train = 150/100 X = (3/2) X kmph
THEREFORE 75/X -75/(3/2)X =125/10 x 60
=> 75/X -50/X =5/24
=> X =25 x 24/5 =120 kmph
ANSWER:A
Answer: A
Question: How many different positive integers are factors of 25?
Options:
A)1
B)5
C)4
D)6
E)8
Rationale: 5*5
Answer : A
Answer: A
Question: How much interest can a person get on Rs. 4500 at 20.1% p.a. simple interest for a period of seven years and six months?
Options:
A)6783.74
B)6783.75
C)6783.76
D)6783.77
E)6783.78
Rationale: I = (4500 * 7.5 * 20.1)/100
= (4500 * 15 * 20.1)/(100 * 2 )
= Rs. 6783.75
Answer: B
Answer: B
Question: Two trains are moving in opposite directions with speed of 60 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds
Options:
A)40
B)42
C)44
D)46
E)48
Rationale: Relative speed = 60+90 = 150 km/hr (Since both trains are moving in opposite directions)
Total distance = 1.1+.9 = 2km
Time = 2/150 hr = 1//75 hr = 3600/75 seconds = 1200/25 = 240/5 = 48 seconds
Answer is E.
Answer: E
Question: A jogger running at 9 km/hr along side a railway track is 280 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)67 sec
B)89 sec
C)36 sec
D)87 sec
E)40 sec
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 280 + 120 = 400 m.
Time taken = 400/10
=40 sec.
Answer: E
Answer: E
Question: Two cyclist start from the same places in opposite directions. One is going towards north at 10kmph and the other is going towards south 40kmph. What time will they take to be 50km apart?
Options:
A)1hr
B)2hrs
C)3hrs
D)5hrs
E)6hrs
Rationale: To be (10+40) km apart, they take 1 hour
To be 50 km apart, they take 1/50 *50 = 1 hrs
Answer is A
Answer: A
Question: Machine A and machine B are each used to manufacture 770 sprockets. It takes machine A 10 hours longer to produce 770 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?
Options:
A)5
B)7
C)9
D)10
E)12
Rationale: Machine B: Takes x hours to produce 770 sprockets
Machine A: Takes (x+10) hours to produce 770 sprockets
Machine B: In 1 hour, B makes 770/x sprockets
Machine A: In 1 hour, A makes 770/(x+10) sprockets
Equating:
1.1(770/(x+10)) = 770/x
847/(x+10) = 770/x
847x = 770x+7700
77x = 7700
x = 100
A makes 770/(110) = 7 sprockets per hour
Answer : B
Answer: B
Question: At a conference, the only events scheduled for the day are seminars and breaks. All seminars are the same length and are 10 times as long as each break. A break must be between two consecutive seminars. If the first seminar begins at 9:00 a.m. and the third one ends at 11:30 a.m., how long will the conference last if there are a total of 6 seminars that day?
Options:
A)hours and 15 minutes
B)hours and 20 minutes
C)hours and 25 minutes
D)hours and 30 minutes
E)hours and 35 minutes
Rationale: Well its like this S B S B S B S B S B S
the interval between 9 am to 11:40 am is 160 min having 3 seminars and 2 breaks .If 1 break is of 5 min than time for 3 seminars = 160 - 2*5=150
Time of 1 seminar =150 /3=50 min .
So calculating for 6 seminars and 5 breaks ,total time comes out to be 5 hrs and 15 min .
Answer is A.
Answer: A
Question: City A's population is 68000, decreasing at a rate of 80 people per year. City B having population 42000 is increasing at a rate of 120 people per year. In how many years both the cities will have same population?
Options:
A)135years
B)140years
C)110years
D)130years
E)120years
Rationale: city A population = 68000
city B population = 42000
68000 decreasing at a rate 0f 80p = 42000 increasing at a rate of 120p
68000-80p=42000+120p
200p=26000
p=130years
ANSWER:D
Answer: D
Question: If 0.003^5 is represented in its shortest possible decimal form, how many 0’s to the right of the decimal point does it contain?
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: 0.003^5= (3*10^-3)^5 = 243*10^-15 = 0.243*10^-12 which would have 12 zeros to the right of the decimal point. The answer is D.
Answer: D
Question: Two buses and a van were employed to transport a class of students on a field trip. 1/5 of the class boarded the first bus. 2/3 of the remaining students boarded the second bus, and the rest of the students boarded the van. When the second bus broke down, 1/2 of the students on the second bus boarded the first bus. What fraction of the class was on board the first bus?
Options:
A)a) 1/2
B)b) 2/3
C)c) 11/15
D)d) 23/30
E)e) 19/30
Rationale: This is a pure ratio question (we aren't given any numbers for anything), so you can just choose any starting number you like, and use it to solve the problem. The best number to pick is almost always the product of all the denominators of your fractions, so here we could start with 30 students. Then we have:
• 1/5 of these, or 6 students, board the first bus
• there are 24 students left. 2/3 of these, or 16 students, board the second bus
• this bus breaks down, and 1/2 of the 6 students, or 3 students, board the first bus
• the first bus now contains 19 out of the original 30 students, so the answer is 19/30
Answer E
Answer: E
Question: how much time does Suresh take to cover a distance of 280 m, if he runs at a speed of 7 km/hr ?
Options:
A)2 min. 24 sec.
B)3 min. 10 sec.
C)1 min. 56 sec.
D)4 min. 32 sec.
E)None of these
Rationale: Explanation :
Solution: s= 7 km/hr = (7*5/18) m/sec = 35/18 m/sec.
Required time = (280*18/35)sec = 144 sec.
= 1min. 24 sec.
Answer : A
Answer: A
Question: Six bells commence tolling together and toll at intervals
of 2,4,6,8,10,12 seconds respectively. In 30 minutes how many
times do they toll together?
Options:
A)14
B)15
C)16
D)17
E)18
Rationale: To find the time that the bells will toll together we have
to take L.C.M of 2,4,6,8,10,12 is 120.
So,the bells will toll together after every 120 seconds
i e, 2 minutes
In 30 minutes they will toll together [30/2 +1]=16 times
ANSWER C
Answer: C
Question: If 8 workers can build 8 cars in 8 days, then how many days would it take 6 workers to build 6 cars?
Options:
A)2
B)4
C)6
D)8
E)12
Rationale: 8 workers can build 1 car per day on average.
1 worker can build 1/8 of a car per day.
6 workers can build 6/8 car per day.
The time required to build 6 cars is 6 / (6/8) = 8 days
The answer is D.
Answer: D
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
Options:
A)76
B)76.5
C)85
D)80
E)none of these
Rationale: Explanation:
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
ANSWER:C
Answer: C
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
Options:
A)84 kmph
B)65 kmph
C)14 kmph
D)77 kmph
E)44 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 42/3 = 14 kmph.
Answer: C
Answer: C
Question: A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 8 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
Options:
A)4.8 hr
B)2.4 hr
C)3.6 hr
D)1.8 hr
E)2.0 hr
Rationale: Explanation:
Part filled by one tap in 1 hour =1/4
Part emptied by second tap 1 hour =1/8
Net part filled by both these taps in 1 hour
=1/3-1/8=5/24
i.e, the cistern gets filled in 24/5 hours =4.8 hrs
Answer: Option A
Answer: A
Question: If |5x-25| = 100, then find the sum of the values of x?
Options:
A)1
B)-2
C)10
D)-3
E)4
Rationale: |5x-25| = 100
5x-25 = 100 or 5x-25 = -100
5x = 125 or 5x = -75
x = 25 or x = -15
sum = 25-15 = 10
Answer is C
Answer: C
Question: In a weight-lifting competition, the total weight of Joe's two lifts was 1500 pounds. If twice the weight of his first lift was 300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift?
Options:
A)225
B)275
C)325
D)350
E)600
Rationale: This problem is a general word translation. We first define variables and then set up equations.
We can define the following variables:
F = the weight of the first lift
S = the weight of the second lift
We are given that the total weight of Joe's two lifts was 1500 pounds. We sum the two variables to obtain:
F + S = 1500
We are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift. We express this as:
2F = 300 + S
2F – 300 = S
We can now plug in (2F – 300) for S into the first equation, so we have:
F + 2F – 300 = 1500
3F = 1,800
F = 600
Answer is E.
Answer: E
Question: If f(x) = 3x^4 - 4x^3 - 2x^2 + 6x , then f(-1) =
Options:
A)-2
B)-1
C)0
D)1
E)2
Rationale: f(-1) = 3(-1)^4 - 4(-1)^3 - 2(-1)^2 + 6(-1) = 3+4-2-6 = -1
The answer is B.
Answer: B
Question: Williams decides to attend a volley ball game with six friends. If the party of seven sits together in seven consecutive seats, and Williams must NOT sit in between two of his friends, how many ways can the seven friends be arranged?
Options:
A)720
B)1440
C)360
D)780
E)1240
Rationale: Williams have to sit at either of the ends.
If Williams sits on the left most corner, then other 6 friends can be arranged in 6! = 720
David can also sit on the other end, then another 6! ways we can arrange.
So total number of ways = 720+720 = 1440
Answer : B
Answer: B
Question: A hat company ships its hats, individually wrapped, in 8-inch by 10-inch by 12-inch boxes. Each hat is valued at $10. If the company’s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes, what was the minimum value of the order?
Options:
A)$3000
B)$1,350
C)$1,725
D)$2,050
E)$2,250
Rationale: Total Volume is 288000
Given LBH = 8*10*12.
the number of hats inside it = 288000/10 * 8 * 12 = 300.
price of each hat is 10 $ then total value is 300 * 10 = 3000.
IMO option A is correct answer..
Answer: A
Question: The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 13 is:
Options:
A)448
B)553
C)542
D)548
E)560
Rationale: Required number = (L.C.M. of 12, 15, 20, 54) + 13
= 540 + 13
= 553.
answer :B
Answer: B
Question: There are 6 persons in an office. A group consisting of 3 persons has to be formed. In how many ways can the group be formed?
Options:
A)15
B)20
C)14
D)12
E)16
Rationale: Number of ways in which the group can be formed = 6C3
= 4*5*6/3*2*1
= 20
Ans- B
Answer: B
Question: Cecilia, Robbie, and Briony all bought stamps. The number of stamps Cecilia purchased was equal to a single digit. The number of stamps only one of them purchased was divisible by 3. The number of stamps one of them bought was an even number. Which of the following could represent the numbers of stamps each purchased?
Options:
A)3, 8, 24
B)7, 9, 17
C)6, 9, 12
D)5, 15, 18
E)9, 10, 13
Rationale: Since in the question stem it states as Only one of them Divisible by 3
We can straight a way eliminate B, because all are ODD.
A,C & D --> more than a number is divisible by 3. Hence eliminate.
E. Single digit number 9 and divisible by 3 we can take this. Hence E Correct.
ANSWER:E
Answer: E
Question: The average of 11 results is 44, if the average of first five results is 49 and that of the last seven is 52. Find the fifth result?
Options:
A)125
B)126
C)127
D)128
E)129
Rationale: 1 to 11 = 11 * 44 = 484
1 to 5 = 5 * 49 = 245
5 to 11 = 7 * 52 = 364
5th = 245 + 364 – 484 = 125
ANSWER:A
Answer: A
Question: How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
Options:
A)2278
B)3779
C)5040
D)2778
E)2813
Rationale: Explanation:
The Word LOGARITHMS is contain 10 letters.
To find how many 4 letter word we can find from that = 10 × 9 × 8 × 7 = 5040.
Answer: C
Answer: C
Question: What is the two-digit number whose first digit is a and the second digit is b?. The number is greater than 9.
I.The number is multiple of 51.
II.The sum of the digits a and b is 6.
Options:
A)I alone sufficient while II alone not sufficient to answer
B)II alone sufficient while I alone not sufficient to answer
C)Either I or II alone sufficient to answer
D)Both I and II are not sufficient to answer
E)Both I and II are necessary to answer
Rationale: Explanation:
From statement I:
A two digit number, greater than 9 and multiple of 51 should be 51 itself.
Because, 2 x 51 = 102 (3 digit number). Therefore, I alone sufficient to answer.
From statement II:
A two digit number, greater than 9 and sum of the digit is 6.
It can be 15, 24, 33, 42, 51. So we cannot determine the required answer from the statement II alone.
Thus, I alone give the answer while II alone not sufficient to answer.
Option A
Answer: A
Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is of the number of students of 8 years of age which is 48. What is the total number of students in the school?
Options:
A)150
B)100
C)280
D)360
E)496
Rationale: Explanation:
Let the number of students be x. Then,
Number of students above 8 years of age = (100 - 20)% of x = 80% of x.
80% of x = 48 +2/3 of 48
80/100x=80
x=100
Answer: B
Answer: B