divelab/Sys2Bench huggingface dataset:
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5%?
Options:
A)399
B)700
C)288
D)500
E)211
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 85
5x/100 + 90 – 6x/100 = 85
x/100 = 5
=> x = 500
Answer: D
Answer: D
Question: A city has a population of 3,00,000 out of which 1,80,000 are males. 50% of the population is literate. If 70% of the males are literate, the number of literate females is :
Options:
A)20,000
B)24,000
C)30,000
D)34,000
E)36,000
Rationale: population - 3,00,000,
males -1,80,000,
females-1,20,000
50% of 3,00,000 literate - so 1,50,000 literate
70% of 1,80,000 literate -so 1,26,000 male literates , so rest s
1,50,000 - 1,26,000 = 24,000
ANSWER:B
Answer: B
Question: If you write down all the numbers from 1 to 100, then how many times do you write 3 ?
Options:
A)11
B)18
C)20
D)21
E)22
Rationale: Explanation:
Explanation:
Clearly, from 1 to 100, there are ten numbers with 3 as the unit's digit- 3, 13, 23, 33, 43, 53, 63, 73, 83, 93; and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.
So, required number = 10 + 10 = 20.
Answer: C
Answer: C
Question: The arithmetic mean of the scores of a group of students in a test was 42. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is?
Options:
A)A)61.4.
B)B)51.7
C)C)33.18
D)D)51.1
E)E)51.2
Rationale: Let the required mean score be x. Then,
20 * 80 + 25 * 31 + 55 * x = 42 * 100
= 1600 + 775 + 55x = 4200
= 55x = 1825
= x = 33.18
Answer:C
Answer: C
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 1 : 2?
A. 48 kmph
Options:
A)33
B)360/7
C)28
D)27/8
E)16
Rationale: Let the distances between city A to B and B to C be x km and 2x km respectively.
Total time taken to cover from A to C
= (x)/40 + (2x)/60 = (3x + 4x)/120 = 7x/120 Average speed = (x + 2x)/(7x/120) = 360/7 kmph.
Answer: B
Answer: B
Question: If 22 men do a work in 55 days, in how many days will 10 men do it?
Options:
A)121
B)123
C)119
D)125
E)127
Rationale: 22 * 55 = 10 * x
x = 121 days
Answer: A
Answer: A
Question: 2 years ago, the average age of a family of 5 members was 16 years. After a baby is born, the average age of family is the same today. Find the present age of the baby.
Options:
A)4 years
B)6 years
C)8 years
D)8 ½ years
E)9 years
Rationale: Hint: (1) First find total age of 5 members 2 years ago (2) Present age of 5 members (3) Total age of 6 members (4) Age of baby = Total age of 6 members - Present age of 5 members
We know that,
Average =Sum of Quantities / Number of Quantities
1) First calculate total age of 5 members 2 years ago = (Average age of 5 members x number of members)
First calculate total age of 5 members 2 years ago = (16 x 5) = 80 years
2) Calculate the present age of 5 members
2 years ago, their total age was 80 years. Present age can be calculated as follows:
Present age of 5 members = [80 + (2 x 5)] = 90 years
3) Calculate total age of 6 members considering baby = (16 x 6 ) = 96 years
4) Age of baby = (96 – 90) = 6 years
ANSWER IS B
Answer: B
Question: A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?
Options:
A)287
B)276
C)279
D)646
E)370
Rationale: 840 = P [1 + (10*3)/100]
P = 646
Answer: D
Answer: D
Question: The cost of 10 kg of mangos is equal to the cost of 24 kg of rice. The cost of 6 kg of flour equals the cost of 2 kg of rice. The cost of each kg of flour is $25. Find the total cost of 4 kg of mangos, 3 kg of rice and 5 kg of flour?
Options:
A)347
B)987
C)1070
D)1371
E)1667
Rationale: Let the costs of each kg of mangos and each kg of rice be $a and $r respectively.
10a = 24r and 6 * 25 = 2r
a = 12/5 r and r = 75
a = 180
Required total cost = 4 * 180 + 3 * 75 + 5 * 25
= 720 + 225 + 125 = $1070
C
Answer: C
Question: Seven years back, a father was 48 years older than his son. At present the father is 4 times as old as the son. How old will the son be three years from now?
Options:
A)16 years
B)17 years
C)18 years
D)19 years
E)20 years
Rationale: Using linear equations to convert the word problem:
** F = fathers current ageS = sons current age
#1 Seven years back, a father was 48 years older than his son: F-7 = 48 + (S - 7)
#2 At present the father is 4 times as old as the son: F = 4*S
How old will the son be three years from now?: S + 3 = ?
With two variables and two linear equations we are able to solve the problem:
(S*4) - 7 = 48 +S -7
3S=48
S = 16
S + 3 = 16 + 3 = 19
Answer: D
Answer: D
Question: Peeta asks Katniss, 'It is 10 9m as per my watch right now.Do you know what will be the time 23, 999, 996 hours later?'
Katniss knows the answer. Do you ?
Options:
A)5pm
B)6pm
C)4am
D)7pm
E)8pm
Rationale: D
7pm
The time after 24, 000, 000 hours will be the same as it is now. We want the time 3 hours before that and thus you can deduct three hours from 9 pm. So the time will be 6 pm.
Answer: D
Question: How many multiples of 7 are there between 700 and 1000, inclusive?
Options:
A)43
B)42
C)22
D)21
E)20
Rationale: There are exactly 301 numbers between 700 to 1000..
701 to 800 = 100
801 to 1000 = 200...Total 300 numbers , count 700 too..
301/7 = 43...
Ans option A.
Answer: A
Question: The difference between the compound interest and simple interest accrued on an amount at the end of three years at the rate of 12% is Rs.381.888. What is the amount?
Options:
A)Rs. 9500
B)Rs. 8400
C)Rs.8000
D)Rs.8200
E)Rs.8500
Rationale: C.I = P[(1+R/100)T - 1]
= P[(1+12/100)3 - 1] = P[(28/25)3 - 1]
= P[(21952/15625) - 1]
= 6327P/15625
S.I = (P x 3 x 12)/100 = Rs. 9P/25
6327P/15625 - 9P/25 = 381.888
=> 702P/15625 = 381.888
=> P = (381.888 x 15625)/702
= Rs. 8500
ANSWER IS E
Answer: E
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)75 kg
B)85 kg
C)95 kg
D)65 kg
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 B
Answer: B
Question: A man has 1044 candles. After burning, he can make a new candle from 9 stubs left behind. Find the maximum number of candles that can be made.
Options:
A)116
B)120
C)130
D)140
E)None
Rationale: Explanation :
Since, 1 candle is made from 9 stubs.
Therefore, from 1044 stubs, 1044/9 i.e 116 candles will be made.
Now, from 116 stubs, 116/9 i.e 12 candles can be made and 8 stubs will be left.
Thus, total stubs left is (12+8) = 20 out of which 20/9 i.e 2 candles can be made and 2 stubs will be left.
Thus, maximum number of candles that can be made is 130 (116+12+2).
Answer : C
Answer: C
Question: Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 5 kg more than Peter. Together the three of them picked 29 kg of chestnuts. How many kilograms of chestnuts did Mary, Peter, and Lucy pick respectively?
Options:
A)6, 11 and 12
B)12, 11 and 6
C)11, 6 and 12
D)12, 6 and 11
E)6, 12 and 11
Rationale: M = 2P
L = P+5
M + P + L = 29
2P + P + (P+5) = 29
P = 6, M = 12, L = 11
Therefore, Mary, Peter, and Lucy picked 12, 6, and 11 kg, respectively.
The answer is D.
Answer: D
Question: A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 10min will be.
Options:
A)60 km/h
B)55 km/h
C)240 km/h
D)70 km/h
E)65 km/h
Rationale: Time=50/60 hr=5/6hr
Speed=48mph
distance=S*T=48*5/6=40km
time=10/60hr=1/6hr
New speed = 40* 6/1 kmph= 240kmph
Answer : C
Answer: C
Question: Company P had 15 percent more employees in December than it had in January. If Company P had 450 employees in December, how many employees did it have in January?
Options:
A) 391
B) 392
C) 410
D) 423
E) 445
Rationale: D = number of employees in December
J = number of employees in January
J x 1.15 = D
J x 1.15 = 450
J = 450/1.15
J = 45,000/115 = 392
Thus B is the correct answer.
Answer: B
Question: Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?
Options:
A)10
B)12
C)14
D)18
E)21
Rationale: Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+26
3x + 6 = x + 26
2x = 20
\inline \therefore x = 10
\inline \therefore Middle number = x + 2 = 10+2 = 12
B
Answer: B
Question: Anand starts from a point P towards point Q, where PQ = 80 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.
Options:
A)(45/7) kmph
B)(160/21) kmph
C)(40/7) kmph
D)(30/7) kmph
E)(65/7) kmph
Rationale: Let the first meeting point be at a distance of x km from P, the remaining distance until Q would be (80-x) km
Anand traveled this x kms in 3 hours, making his speed x/3 kmph
Ram traveled the same x kms in 2 hours, making his speed x/2 kmph
So, in 6 hours:
Anand will cover=6x/3=2x km
Ram will cover=6x/2=3x km
And between their first meeting point and second, they both together covered a distance of 2(90-x) km.
2x+3x=2(80-x)
5x=160-2x
7x=160
x=160/7 km
Anand's speed=x/3=160/(3*7)=160/21 kmph
Ans:B
Answer: B
Question: The sum of 5 different positive 2-digit integers is 130. What is the highest possible value of the largest of these integers?
Options:
A)88
B)84
C)78
D)74
E)68
Rationale: sum of 5 different 2 digit integers=130
to find out the largest number, we need to make other 4 numbers to the smallest as possible.
smallest 2 digit number is 10
=>10+11+12+13+n=130
=>n=130-46=84
Answer is B
Answer: B
Question: For any triangle T in the xy–coordinate plan, the center of T is defined to be the point whose x–coordinate is the average (arithmetic mean) of the x–coordinates of the vertices of T and whose y–coordinate is the average of the y–coordinates of the vertices of T. If a certain triangle has vertices at the points (0,0) and (9,3) and center at the point (4,3), what are the coordinates of the remaining vertex?
Options:
A)(3,4)
B)(3,9)
C)(4,9)
D)(6,4)
E)(3,6)
Rationale: Let (a,b) be the remaining vertex.
x: 0 + 9 + a = 3*4. Then a = 3.
y: 0 + 3 + b = 3*3. Then b = 6.
The answer is E.
Answer: E
Question: What could be the maximum value of Q in the following equation?
5P9 + 3R7 + 2Q8 = 1114
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: 5 P 9
3 R 7
2 Q 8 +
———-
11 1 4
———-
=>2+P+Q+R=11
so at max Q, P=R=0,
therefore Q=11-2=9.
ANSWER:E
Answer: E
Question: In a local school district, the high school and middle school each received r dollars toward funding for the student arts program. The high school enrolled 150 students and the middle school enrolled 75 students. Later, the middle school transferred s dollars to the high school so that they would have received the same funding per student. Which of the following is equivalent to s?
Options:
A)r/8
B)r/5
C)r/2
D)r/3
E)r/9
Rationale: Total per head = 2r/225
After s transfer both schools have total for head.
So at High School it will be:
r+s = (150)* (2r/225) = 12r/9=4r/3
i.e. s = 4r/3 - r/1 =4r-3r/3=r/3
Answer :D
Answer: D
Question: A chemical supply company has 60 liters of a 25% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution?
Options:
A)12
B)15
C)20
D)24
E)30
Rationale: 60 liters of a 25% HNO3 solution means HNO3 = 15 liters in 60 liters of the solution.
Now, let x be the pure HNO3 added.
As per question,
15 + x = 50% of (60 + x)
or x =30. Hence, E
Answer: E
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
Options:
A)65 seconds
B)14 seconds
C)14 seconds
D)12 seconds
E)12 seconds
Rationale: Speed of the boat downstream
= 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m
= 60/5 =12 seconds.
Answer: D
Answer: D
Question: 50, 47, 45, 42, 40, 37, ?
Options:
A)36
B)35
C)34
D)33
E)32
Rationale: This is an alternating number subtraction series. The pattern is -3, -2, -3, -2, ....
The answer is B.
Answer: B
Question: A 4-letter code word consists of letters X, Y, and Z. If the code includes all the three letters, how many such codes are possible?
Options:
A)36
B)72
C)48
D)24
E)18
Rationale: Note that the correct answer to this question is 36, not 72.
X-XYZ can be arranged in 4!/2!=12 ways;
Y-XYZ can be arranged in 4!/2!=12 ways;
Z-XYZ can be arranged in 4!/2!=12 ways;
Total: 12+12+12=36.
Answer: A.
Answer: A
Question: If y exceeds x by 22%, then x is less than y by?
Options:
A)18 2/8%
B)18 8/3%
C)18 2/61%
D)76 2/3%
E)17 2/3%
Rationale: X=100	y=122
122------22
100-------? => 18 2/61%
Answer:C
Answer: C
Question: Two persons starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 12.5km apart, if they walk in the same direction?
Options:
A)17 hrs
B)22 hrs
C)25 hrs
D)12 hrs
E)14 hrs
Rationale: The relative speed of the boys = 5.5kmph â€“ 5kmph
= 0.5 kmph
Distance between them is 12.5 km
Time= 12.5km / 0.5 kmph = 25 hrs
Answer : C.
Answer: C
Question: If n is a positive integer, then n(n-1)(n-2) is +ve even
Options:
A)odd whenever n is odd
B)divisible by 3 only when n is odd
C)divisible by 4 whenever n is even
D)even only when n is odd
E)even only when n is even
Rationale: n*(n-1)*(n-2)= +ve even integer divisible by 4 ( e.g 6,7&8)
C
Answer: C
Question: In a friendship gang Andrew has 8 gang, in how many ways can he invite one or more of the gang to his house?
Options:
A)245
B)255
C)260
D)267
E)459
Rationale: Andrew can select one or more than one of his 8 gang.
=> Required number of ways = 28 – 1= 255.
B
Answer: B
Question: What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?
Options:
A)Rs.8000
B)Rs.8400
C)Rs.7500
D)Rs.7800
E)None
Rationale: 8820 ---- 441
100 ---- ? => 5%
x *105/100 * 105/100 = 8820
x*1.1025=8820
x=8820/1.1025 => 8000
ANSWER:A
Answer: A
Question: Find the sum of prime numbers lying between 60 and 72?
Options:
A)198
B)201
C)199
D)272
E)None
Rationale: Solution
Required sum	= 61 + 67 + 71)
= 199.
Answer C
Answer: C
Question: Workers decided to raise Rs.3lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25lacs. How many workers were they?
Options:
A)400
B)600
C)500
D)700
E)800
Rationale: N * 50 = (325000 - 300000) = 25000
N = 25000 / 50
= 500
C
Answer: C
Question: What is the greatest power that 7 can be raised to so that the resulting number is a factor of 21!?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: the number of 7s in 21!= 21/7=3..
ans B
Answer: B
Question: In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Options:
A)2kmph
B)3kmph
C)8kmph
D)9kmph
E)7kmph
Rationale: Speed in still water = (11+5)/2
= 8 kmph
Ans- C
Answer: C
Question: A, B, C hired a car for Rs. 520 and used it for 7,8 and 11 hours respectively. Hire charges paid by B were :
Options:
A)160
B)180
C)220
D)225
E)None
Rationale: Sol.
A : B : C = 7 : 8 : 11.
Hire charges paid by B = Rs. [520 * 8/26] = Rs.160
Answer A
Answer: A
Question: If [B] denotes the least integer greater than or equal to B and [B] = 0, which of the following statements must be true?
Options:
A)B = 0
B)0 <= B < 1
C)0 < B <= 1
D)-1 < B <= 0
E)-1 <= B < 0
Rationale: The answer for this is 0 < = B < = 1
However it is not available in the options. The match to the above is-1 < B <= 0
Answer = D
Answer: D
Question: The average of non-zero number and its square is 5 times the number. The number is:
Options:
A)9
B)7
C)8
D)5
E)3
Rationale: Let the number be x. Then,
(x + x2)/2 = 5x => x2 - 9x = 0
=> x(x - 9) = 0
=> x = 0 or x = 9
So, the number is 9.
Answer: A
Answer: A
Question: Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 9 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
Options:
A)67
B)88
C)18
D)26
E)12
Rationale: Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/9
=> 1/x = 1/6 - 1/9 = (3 - 2)/18 = 1/18
=> x = 18. Answer:C
Answer: C
Question: If 7 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed?
Options:
A)588
B)263
C)120
D)160
E)1260
Rationale: parallelogram can formed by 2 horizontal and 2 vertical lines
for horizontal 7c2
for vertical 8c2
total parallelogram is 7 c2*8c2=21*28
=588
ANSWER:A
Answer: A
Question: The least number which is a perfect square and is divisible by each of the numbers 16,20, and 24, is :
Options:
A)1600
B)3600
C)6400
D)11400
E)None of these
Rationale: Solution
The least number divisible by 16, 20, 24
= L.C.M. of 16, 20, 24 = 240 = 2 × 2 × 2 × 2 × 3 × 5.
To make it a perfect square it must be multiplied by 3 × 5.
∴ Required number = 240 × 3 × 5 = 3600. Answer B
Answer: B
Question: In 2triangle, the ratio of the areas is 4:3 and that of their heights is 3:4. Find the ratio of their bases?
Options:
A)10:8
B)11:8
C)16:9
D)17:19
E)17:10
Rationale: Given a1/a2 =4/3, h1/h2=3/4
also, we know that
a1/a2=(1/2×b1×h1)/(1/2×b2×h2)
on substituting in above equation, we get
b1/b2= 16/9
therefore b1:b2= 16:9
C
Answer: C
Question: My age is two year more than twice than of Ram. If I am 34 years old, how old is Ram?
Options:
A)18
B)14
C)16
D)20
E)12
Rationale: myage = 2 + 2*Ram
34 = 2 + 2*Ram
2(Ram) = 32
Ram = 16
ANSWER:C
Answer: C
Question: The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to r% of stall’s revenue and accounted for s% of sales of juice tetra packs. Which of the following expresses r in terms of s?
Options:
A)100s/(150 – s)
B)200s/(250-s)
C)200s/(300-s)
D)250s/(400-s)
E)300s/(500-s)
Rationale: 1. Let the number of units sold be 100. Then n units of A are sold and (100-n) units of B are sold.
Total revenue= Revenue due to A + Revenue due to B
= (No.of units of A sold * Cost/unit of A) + (No.of units of B sold * cost/unit of B)
= s *1 + (100-s) *1.5
= s + (150-1.5s) --- (1)
2. But we know, revenue due to A = r%. of the total revenue --- (2)
3. To express r in terms of s we need to relate (1) and (2)
4. r% = s / ( s + (150-1.5s))
or r= 100s / 150-0.5s = 200s/(300-s)
C
Answer: C
Question: In an animal behavior experiment, 50 tagged white pigeons and 300 tagged gray pigeons were released from a laboratory. Within one week, 88 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory?
Options:
A)80.5
B)82
C)81.75
D)85
E)86.5
Rationale: Weighted mix method is best here....
Ratio is 1:6 for 88:80.5...
So the answer required = 80.5+ (88-80.5)*1/6=80.5+7.5*1/6
80.5+1.75=81.75
C
Answer: C
Question: The product of all the prime numbers less than 15 is closest to which of the following powers of 10?
Options:
A)10^2
B)10^4
C)10^7
D)10^6
E)10^5
Rationale: Quickly approximate
2, 3, 5, 7, 11,13
3*10^4
A
Answer: A
Question: What is the difference between the compound interests on Rs. 5000 for 1 years at 4% per annum compounded yearly and half-yearly?
Options:
A)Rs. 2.04
B)Rs. 3.06
C)Rs. 4.80
D)Rs. 6.30
E)Rs. 8.30
Rationale: As per formula it should be,
C.I. when interest = 5304-5000 = 304
compounded yearly
C.I. when interest is = 5306.04-5000 = 306.04
compounded half-yearly
Difference = Rs. (306.04 - 304) = Rs. 2.04
answer :A
Answer: A
Question: What is the smallest number W which when increased by 5 is completely divisible by 8, 11 and 24?
Options:
A)264
B)259
C)269
D)270
E)282
Rationale: This question includes a number of great Number Property shortcuts that you can take advantage of:
1) The question asks for the SMALLEST number that, when increased by 5 is divisible by 8, 11 and 24. Since the answers are numbers, we can TEST THE ANSWERS.
2) Any number that is divisible by 24 is ALSO divisible by 8, so we really just need to consider the 11 and the 24.
3) To be divisible by 24, the end number MUST be EVEN. Since we're adding 5 to get to that end number, the starting number MUST be ODD.
The last shortcut allows us to eliminate Answers A, D and E. Between Answers B and C, TESTING B first will prove that, when increased by 5, the end sum is divisible by both 11 and 24.
Final Answer:
B
Answer: B
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 142 m length?
Options:
A)82.1 sec.
B)12.6 sec
C)19.1 sec.
D)17.1 sec.
E)42.1 sec.
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 142 = 252 m.
Required time = 252/20 = 12.6 sec.
Answer: B
Answer: B
Question: The sum of three consecutive odd natural numbers, each divisible by 3 is 66. What is the largest among them?
Options:
A)21
B)24
C)25
D)36
E)57
Rationale: Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6
Given, X + X+3 + X+6 = 66
3X = 57
X = 19
The numbers are 19, 22, 25
Therefore the largest number is 25
Answer C.
Answer: C
Question: Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together?
Options:
A)2207 ways
B)1440 ways
C)1220 ways
D)2810 ways
E)2760 ways
Rationale: Explanation:
In the word, "MATERIAL" there are three vowels A, I, E.
If all the vowels are together, the arrangement is MTRL'AAEI'.
Consider AAEI as one unit. The arrangement is as follows.
M T R L A A E I
The above 5 items can be arranged in 5! ways and AAEI can be arranged among themselves in 4!/2! ways.
Number of required ways of arranging the above letters = 5! * 4!/2!
= (120 * 24)/2 = 1440 ways.
Answer: B
Answer: B
Question: A bike covers a certain distance at the speed of 16km/h in 2 hrs. If the bike was to cover the same distance in approximately 4 hrs, at what approximate speed should the bike travel?
Options:
A)8 km/h
B)9 km/h
C)7 km/h
D)6 km/h
E)10 km/h
Rationale: Ans.(A)
Sol. Total distance = 16 × 2 = 32 km
Now speed = 32/4 = 8 km/h
Answer: A
Question: A snooker tournament charges $40.00 for VIP seats and $15.00 for general admission (“regular” seats). On a certain night, a total of 320 tickets were sold, for a total cost of $7,500. How many fewer tickets were sold that night for VIP seats than for general admission seats?
Options:
A)212
B)200
C)220
D)230
E)240
Rationale: let no of sits in vip enclosure is x then x*40 +15( 320-x) =7500 or 25x = 7500 -4800 , x = 2700/25 =108
vip =108 general 212
A
Answer: A
Question: Mariah has decided to hire three workers. To determine whom she will hire, she has selected a group of 15 candidates. She plans to have one working interview with 3 of the 15 candidates every day to see how well they work together. How many days will it take her to have working interviews with all the different combinations of job candidates?
Options:
A)720
B)120
C)300
D)360
E)333
Rationale: 360.
Answer D
Answer: D
Question: When divided by 5, x has a remainder of 4 and y has a remainder of 3. Which of the following could be the remainder when x + y is divided by 10?
Options:
A)6
B)7
C)8
D)9
E)0
Rationale: x = 5k+4 and y = 5j+3
x+y = 5(j+k) + 7
When divided by 10, the remainder is either 7 or 2.
The answer is B.
Answer: B
Question: Brandon has cans of both diet soda as well as regular soda. The ratio of diet soda to regular soda is 3 to 7. He has 12 more cans of soda than diet. How many cans of diet soda does he have left?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: Let x equal the cans of diet soda, and y equal the cans of regular soda.
Since we want to solve for x (cans of diet soda), we convert the ratio from 3/7 to 7/3.
So, we know that y = 7/3x.
We also know that y = x + 12.
We can simplify:
x + 12 = 7/3x
To isolate x, we get:
4/3x = 12
And to solve for x, we get:
x = 9
Answer: D
Answer: D