divelab/Sys2Bench huggingface dataset:
Question: What is the next number of the following sequence
1,2,3,5,8,13,?
Options:
A)25
B)21
C)20
D)24
E)28
Rationale: 1+2=3
2+3=5
3+5=8
5+8=13
8+13=21
therefore next no. is 21
ANSWER:B
Answer: B
Question: A child must place 3 different toys in 4 different bins. If any of the toys can go in any of the bins, in how many ways can the child place the toys into the bins?
Options:
A)6^6
B)6^4
C)4^6
D)4^3
E)6^4-4^6
Rationale: there are 4 different bins and each of the toy can go to any of these bins..
so answer 4âˆ—4âˆ—4=4^3
ANSWER:D
Answer: D
Question: The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is?
Options:
A)12
B)14
C)16
D)18
E)21
Rationale: 3:4
Total parts = 7
= 7 parts --> 28 (7 × 4 = 28)
= 1 part ---->4 (1 × 4 = 4)
= The greater of the two number is = 4
= 4 parts ----> 16 (4 × 4 = 16)
C
Answer: C
Question: A boat goes 8 km upstream in 24 minutes. The speed of stream is 4 km/hr. The speed of boat in still water is:
Options:
A)24 km/hr
B)29 km/hr
C)27 km/hr
D)25 km/hr
E)26 km/hr
Rationale: Speed upstream =8(24/60) = 20 km/hr
Speed of the stream = 4 km/hr
speed of boat in still water = (20+4) = 24 km/hr
Answer: A
Answer: A
Question: The sale price sarees listed for Rs.500 after successive discount is 10% and 5% is?
Options:
A)427.5
B)277
C)342
D)882
E)212
Rationale: 500*(90/100)*(95/100) = 427.5
Answer: A
Answer: A
Question: A merchant has 1000kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is
Options:
A)348
B)600
C)277
D)188
E)112
Rationale: Rule of Allegation
Answer with Explanation: Profit on I kind (%) (c) Profit of II kind (d) 8 18
Mean Price (m) d-m (18-14) = 4 14 m-c (14-8) = 6
Ratio of Profits on I and II kind = 4:6 = 2:3
Step (ii) Quantity sold at 18% profit = (3/5 x 1000) kg = 600 kg.
Answer:B
Answer: B
Question: Larry, Michael, and Doug have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?
Options:
A)21
B)42
C)120
D)504
E)5040
Rationale: If you get confused about combinations, there's a simple way to count these combinations as well, by counting the number of ways 5 can be summed with 3 numbers.
{5,0,0} = 3 possibilities.
{4,1,0} = 6 possibilities.
{3,2,0} = 6 possibilities.
{3,1,1} = 3 possibilities.
{2,2,1} = 3 possibilities.
Total = 21 possibilitieS
ANSWER:A
Answer: A
Question: A class has three girls and three boys. These students line up at random, one after another.
What is the probability that no boy is right next to another boy, and no girl is right next to
another girl?
Options:
A)1 /20
B)1 /12
C)1 /10
D)3 /10
E)1 /2
Rationale: We pick the students in order. The first choice is always okay. There is a probability
3/5 that the second choice is okay; for example, if you picked a boy first then there are two boys
and three girls left. Similarly the probabilities that the remaining choices are okay is 1/2 , 2/3 , 1/2,1. The answer is 1/10 , the product of all these probabilities.
correct answer C
Answer: C
Question: In an examination 35% of the students passed and 260 failed. How many students appeared for the examination?
Options:
A)A)540
B)B)400
C)C)700
D)D)650
E)E)840
Rationale: Let the number of students appeared be x
then, 65% of x = 260
65x/100 = 260
x = 260*100/65 = 400
Answer is B
Answer: B
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
Options:
A)2000
B)2772
C)8122
D)2888
E)2211
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: A
Answer: A
Question: In a fuel station the service costs $2.20 per vehicle and every liter of fuel costs $0.70. Assuming that you fill up 3 mini-vans and 2 trucks, what will be the total cost, if a mini-van's tank is 65 liters and a truck's tank is 120% bigger and they are all empty?
Options:
A)$341.50
B)$344.60
C)$347.70
D)$350.80
E)$353.90
Rationale: The service cost of 3 vans and 2 trucks is 5*2.20 $11.00
The fuel in 3 vans is 3*65 = 195 liters
The fuel in 2 trucks is 2*65*2.2 = 286 liters
The total fuel (vans + trucks) = 481 liters
The total fuel cost is 481*0.7 = $336.70
The total cost is $336.70 + $11.00 = $347.70
The answer is C.
Answer: C
Question: GOOD is coded as 164 then BAD coded as 21.if ugly coded as 260 then DAB?
Options:
A)20
B)21
C)22
D)23
E)24
Rationale: GOOD=(7+15+15+4)*4=164
BAD= (2+1+4)*3=21
UGLY= (21+7+12+25)*4=260
coding follows
(sum of position of alphabets)*(no. of letters in the given word)
so,
DAB=(4+1+2)*3= 21
ANSWER:B
Answer: B
Question: A family has a man, his wife, their four sons and their wives and one daughter. The family of every son also has 3 sons and one daughter. Find out the total number of female members in the family ?
Options:
A)15
B)10
C)12
D)16
E)13
Rationale: Explanation:
1) Man's wife. = 1
2) Man's 4 son's wives. = 4
3) Man's daughter. = 1
4) 4 son's has each one daughter. = 4
Therefore, total number of female members in the family = 1+4+1+4 = 10.
Answer B
Answer: B
Question: In five football games thus far this season, Barry has run for 98, 107, 85, 89, and 91 yards. At a minimum, how many yards M will he need to gain this Sunday if he wants to keep his season average above 100 yards?
Options:
A)101
B)116
C)M=130
D)M=131
E)M=141
Rationale: Sorry the answer M=141 is D.
Answer: D
Question: At a local beach, the ratio of little dogs to average dogs to enormous dogs is 3:4:8. Late in the afternoon, the ratio of little dogs to average dogs doubles and the ratio of little dogs to enormous dogs increases. If the new percentage of little dogs and the new percentage of average dogs are both integers and there are fewer than 30 total dogs at the beach, which of the following represents a possible new percentage of enormous dogs?
Options:
A)25%
B)40%
C)55%
D)50%
E)70%
Rationale: Little Dogs(L), Average Dogs(A) and Enormous Dogs (E)
The initial ratio for L:A:E :: 3:4:8
Initial Total dogs = 15X ( x assumed; 2+5+8= 15), Since the total dogs are less than 30 therefore initial total value has to be 15
L = 3, A = 4 E = 8
L:A= 3:4
This ratio doubles
Hence New Dog count is
L= 6 , A = 4 E= X: Also 6+4+x<30
We need to Find X*100/(4+6+X)
Now it says that new percentage of little dogs and Average dogs is an integer
%L = 6*100/(10+x) %A = 4*100/(10+x); Only Value for X is 10 ; 9+x<30 and % integer
Therefore, Enormus Dogs % is = 10*100/(20) = 50%
D
Answer: D
Question: Two trains 121 meters and 153 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
Options:
A)7.19
B)6.8
C)7.2
D)7.15
E)7.11
Rationale: T = (121 + 153)/ (80 + 65) * 18/5
T = 6.8
Answer:B
Answer: B
Question: A profit of Rs. 500 is divided between X and Y in the ratio of 1/2:1/3 . What is the difference between their profit shares ?
Options:
A)Rs. 200
B)Rs. 100
C)Rs. 300
D)Rs. 50
E)Rs. 90
Rationale: A profit of Rs. 500 is divided between X and Y in the ratio of 1/2 : 1/3 or 3:2.
so profits are 300 and 200.
difference in profit share = 300-200=100
ANSWER:B
Answer: B
Question: How many prime numbers are between 76/8 and 124/5?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 76/8 = 38/4 = 19/2 = 10-
124/5 = 25-
Prime numbers between 10 and 29 are 11, 13, 17, 19, and 23
- sign signifies that the number is marginally less .
Answer E
Answer: E
Question: The following sets each have a mean of 8 and the standard deviations are given in variable form.
Set I = {8, 8, 8, 8, 8, 8}, standard deviation = A
Set II = {2, 2, 2, 14, 14, 14}, standard deviation = B
Set III = {5, 6, 7, 9, 10, 11}, standard deviation = C
Rank these three standard deviations from least to greatest.
Options:
A)A, B, C
B)B, C, A
C)C, A, B
D)C, B, A
E)A, C, B
Rationale: The answer should be E as the mean is least deviated in Set I followed by Set III and then Set II.
Answer: E
Question: 33 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be :
Options:
A)84 m
B)88 m
C)42 m
D)137 m
E)None
Rationale: Sol.
Let the length of the wire b h.
Radius = 1/2 mm = 1/20 cm. Then,
22/7 * 1/20 * 1/20 * h = 33 ⇔ = [33 * 20 * 20 * 7 / 22] = 4200cm = 42 m.
Answer C
Answer: C
Question: If the President and Vice President must sit next to each other in a row with 3 other members of the Board, how many different seating arrangements are possible?
Options:
A)48
B)240
C)300
D)360
E)720
Rationale: We need to take President and VP as one unit. Therefore we have 3 people to arrange=4! ways
Also, we both President and VP can be arranged in 2 ! ways.
Reqd no of ways=4!*2!=48ways
Answer A
Answer: A
Question: Tickets numbered from 1 to 24 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bears a number which is a multiple of 3?
Options:
A)1/3
B)2/5
C)3/10
D)3/7
E)1/7
Rationale: Here, S = [1, 2, 3, 4, …., 19, 20, 21, 22, 23, 24]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18, 21, 24]
P (E) = n (E) / n (S) = 8 / 24 = 1/3
The answer is A.
Answer: A
Question: 25 is a perfect square and x is also a perfect square. when x is added to 25 and 1 is substrate from it will give an answer which is also a perfect square. then what is the square root of x?
Options:
A)6
B)2
C)3
D)5
E)4
Rationale: here
6*6=36, 25+36-1=60
2*2=4, 25+4-1=28
3*3=9, 25+9-1=33
5*5=25, 25+25-1=49
4*4=16, 25+16-1=40
So 49 is the perfect square of 7
so the answer is D
Answer: D
Question: The average height of the four Torres towers is 800 feet. If the four Torres towers have a median height of 900 feet, what is the greatest possible height of the shortest building of the four?
Options:
A)100 feet
B)300 feet
C)500 feet
D)600 feet
E)800 feet
Rationale: a1≤a2≤a3≤a4;
The average height of the four Torres towers is 800 feet: a1+a2+a3+a4=4∗800
The median height of 900 feet: a2+a32=900 --> a2+a3=1800
Substitute a2+a3=1800 into a1+a2+a3+a4=4∗80: a1+1800+a4=4∗800 --> a1+a4=1400
To maximize a1a1 we should minimize a4a4. Minimum value of a4a4 is 900 (the median value), thus the maximum value of a1a1 is 1400 - 900 = 500.
Answer: C
Answer: C
Question: The L.C.M of 2/3, 3/ 5, 4/7, 9/13 is :
Options:
A)45
B)28
C)36
D)42
E)32
Rationale: Required L.C.M =L.C.M. of 2,3,4,9/H.C.F. of 3,5,7,13 =36/1=36
Answer is C
Answer: C
Question: 49, 98, 686, 1372....
Options:
A)9052
B)8711
C)9279
D)9604
E)9086
Rationale: 49 x 2 = 98
98 x 7 = 684
684 x 2 =1372
1372 x 7 = 9604
Answer = D
Answer: D
Question: A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?
Options:
A)Rs. 14,000
B)Rs. 12,000
C)Rs. 30,000
D)Rs. 40,000
E)Rs. 50,000
Rationale: [1000 + (X-4000) * (2.5/100)] - X * (5/100) = 600
X = 12000
ANSWER:B
Answer: B
Question: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
Options:
A)87
B)98
C)30
D)28
E)37
Rationale: 20 + 24 + 8 * 2
= 60/2
= 30
Answer:C
Answer: C
Question: If an article is bought at a profit of 15% and sold at a loss of 15% what is my total profit percent or loss percent?
Options:
A)1.25
B)2.25
C)3.25
D)4.25
E)5.25
Rationale: in the case if profit and loss is given same then in that case we can put the direct formula given as
(15*15)/100=2.25%
ANSWER:B
Answer: B
Question: A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more thanC. Out of a total profit of Rs. 35,000, A receives?
Options:
A)14700
B)14298
C)23877
D)27297
E)17281
Rationale: Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000 <=> 3x = 36000 <=>
x = 12000.
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
A's share = Rs. (35000 * 21/50 ) = Rs. 14,700.
Answer: A
Answer: A
Question: Joke is faster than Paul, Joke and Paul each walk 24 KM. The sum of their speed is 7 Km per hour. And the sum of times taken by them is 14 hours. Then, Joke speed is
Options:
A)2
B)8
C)7
D)3
E)0
Rationale: Speed=DistanceTimeSpeed=DistanceTime
let the speed of joke x then speed of paul will be 7-x
24x+247−x=1424x+247−x=14
Try to plugin the values from the options. If Joke speed is 4 the paul is 3.
Answer:D
Answer: D
Question: Line J has a y-intercept of 10 and passes through point (a,b). What is the slope of Line J in terms of a and b?
Options:
A)(a−6)/b
B)(a−b)/6
C)(6−a)/b
D)(b-10)/a
E)(b−6)/a
Rationale: You know that the line goes through point (a,b) and the y-intercept of 10 tells you that the line also goes through point (0,10).
slope m = (y-y1)/(x-x1) = (b-10)/(a-0)= (b-10)/a
D
Answer: D
Question: The product of n-1 consecutive positive integers is always divisible by
Options:
A)n^2 -1
B)(n-1)!
C)2n +1
D)n^2 + 1
E)n!
Rationale: Plug in some vlues and check -
Product of first 2 number is 2*1
Product of first 3 number is 3*2*1
Product of first 4 number is 4*3*2*1
Product of first 5 number is 5*4*3*2*1
So, The product of first n natural numbers is always divisible by n! , answer will be (B)
Answer: B
Question: If the Average of 10 consecutive integers is 20.5 then the 10th integer is :-
Options:
A)15
B)20
C)23
D)24
E)25
Rationale: The average falls between the 5th and 6th integers,
integer 5 = 20, integer 6 = 21.
Counting up to the tenth integer
we get 25.
ANSWER:E
Answer: E
Question: If A and B are two events such that P (A) = 3/4, P (B) = 1/4 and P (A n B) = 3/8,
find P (not A and not B).
Options:
A)A)3/7
B)B)3/8
C)C)3/9
D)D)3/10
E)E)3/11
Rationale: P(not A and not B) = 1 - (P(A) + P(B) - P(AB))
which you might find somewhere in your text.
Substituting in our probabilities we get:
P(not A and not B) = 1 - (3/4 + 1/4 - 3/8)
P(not A and not B) = 1 - (5/8)
P(not A and not B) = 3/8.
B
Answer: B
Question: How many arrangements of the letters of the word BEGIN can be made, without changing the place of the vowels in the word?
Options:
A)5 ways
B)6 ways
C)7 ways
D)9 ways
E)11 ways
Rationale: E,I fixed. Consonants can be arrangements in 3P3 = 3! = 6 ways
B)
Answer: B
Question: The sum of the numbers is 264. If the first number be twice the second and third number be one-third of the first, then the second number is:
Options:
A)48
B)54
C)72
D)84
E)90
Rationale: Explanation:
Let the second number be x. Then, first number = 2x and third number = 2x/3.
2x + x + 2x/3 = 264
11x/3 = 264
x = 72
ANSWER IS C
Answer: C
Question: A train is 360 meter long is running at a speed of 54 km/hour. In what time will it pass a bridge of 140 meter length?
Options:
A)33.33 seconds
B)38 seconds
C)40 seconds
D)88 seconds
E)19 seconds
Rationale: Speed = 54 Km/hr = 54*(5/18) m/sec = 15 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (1/15) = 33.33 seconds
Answer: A
Answer: A
Question: A reduction of 24% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
Options:
A)2.8
B)3.2
C)2.5
D)2.1
E)2.9
Rationale: 100*(24/100) = 24 --- 10
? --- 1 => Rs.2.4
100 --- 76
? --- 2.4 => Rs.3.2
Answer: B
Answer: B
Question: In a BCCI meeting there are 15 people. All shake hands with each other once. How many handshakes will be there altogether?
Options:
A)28
B)14
C)15
D)19
E)18
Rationale: There will be n-1 handshakes as A person will shake hands with all the other members.
=15-1=14
Answer:B
Answer: B
Question: Find the area of a parallelogram with base 24 cm and height 12 cm?
Options:
A)297 cm2
B)384 cm2
C)672 cm2
D)267 cm2
E)288 cm2
Rationale: Area of a parallelogram
= base * height
= 24 * 12
= 288 cm2
Answer: E
Answer: E
Question: P and Q can complete a work in 80 days and 48 days respectively. P alone started the work and Q joined him after 8 days till the completion of the work. How long did the work last?
Options:
A)35 days
B)10 days
C)14 days
D)22 days
E)26 days
Rationale: Explanation :
Work done by P in 1 day = 1/80
Work done by Q in 1 day = 1/48
Work done by P in 8 days =8 Ã— (1/80) = 1/10
Remaining work = 1 â€“ 1/10 = 9/10
Work done by P and Q in 1 day = 1/80 + 1/48 = 1/30
Number of days P and Q take to complete the remaining work = (9/10) / (1/30) = 27
Total days = 8 + 27 = 35
Answer : Option A
Answer: A
Question: How many pairs (e, e+1) have one or more prime factors common, where e is an integer and 2 ≤ e ≤9 ?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: e and e+1 are consecutive integers.
Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.
Answer: A.
Answer: A
Question: A bundle of flowers consists of 5 focal flowers and 7 foliage fillers. If a bouquet is created with 3 focal flowers and 5 foliage fillers, in how many ways can an original bouquet be formed?
Options:
A)29
B)30
C)45
D)204
E)210
Rationale: Choose 3 focal flowers from 5 focal flowers and choose 3 foliage fillers from 5 foliage fillers:
3C5 * 5C7 = 10*21 = 210
Ans: D
Answer: D
Question: In ten years, David will be four times as old as Aaron. Twenty years ago, David was twice as old as Ellen. If David is eleven years older than Ellen, how old is Aaron?
Options:
A)3–5
B)6–10
C)11–15
D)16–20
E)21–25
Rationale: Let David's present age be 'd', Aaron's present age be 'a' and Ellen's present age be 'e'
In ten years, David will be four times as old as Aaron --> d+10 = 4(a+10)
Twenty years ago, David was twice as old as Ellen --> d-20 = 2(e-20)
David is seven years older than Ellen --> d = e + 11
e+11-20 = 2e-40
e-9 = 2e-40
e = 31
d = 42
52 = 4a + 40
a = 3
Answer: A
Answer: A
Question: Trapezoid JKLM in the x-y plane has coordinates J = (–3, –4), K = (–3, 1), L = (5, 7), and M = (5, –4). What is its perimeter?
Options:
A) 34
B) 36
C) 38
D) 40
E)(F) 42
Rationale: JK = 5
LM = 11
KL =using distance formula 10
JM = using distance formula 8
Sum of all is 34
A
Answer: A
Question: Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 8.5 km apart, if they walk in the same direction?
Options:
A)12 hrs
B)14 hrs
C)15 hrs
D)17 hrs
E)None
Rationale: Sol.
to be 0.5 km apart, they take 1 hour.
To be 8.5 km apart, they take [1/0.5 * 8.5] hrs = 17 hrs.
Answer D
Answer: D
Question: A car travels the first 1/3 of certain distance with a speed of 10km/hr the next 1/3 distance with a speed of 12 km/hr, and the last 1/3 distance with a speed of 60 km/hr. the average speed of the car for the whole journey is?
Options:
A)12km/hr
B)15km/hr
C)89km/hr
D)52km/hr
E)79km/hr
Rationale: Let the whole distance travelled be x km
and the average speed of the car for he whole journey be y km/hr
then (x/3)/10+(x/3)/12+(x/3)/60=x/y
x/30+x/36+x/180=x/y
1/15y=1
y=15km/hr
Answer(B)
Answer: B
Question: A store owner estimates that the average price of type A products will increase by 25% next year and that the price of type B products will increase by 20% next year. This year, the total amount paid for type A products was $4500 and the total price paid for type B products was $8300. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
Options:
A)$14,755
B)$15,585
C)$16,000
D)$16,225
E)$17,155
Rationale: cost of type A products next year = 1.25 * 4500 = 5625
cost of type B products next year = 1.2 * 8300 = 9960
total 5625 + 9960 = 15585 option B
Answer: B
Question: 5⁄7 of 4⁄15 of a number is 8 more than 2⁄5 of 4⁄9 of the same number. What is half of that number?
Options:
A)630
B)315
C)210
D)105
E)None of these
Rationale: Let the number be x.
∴ 5⁄7 × 4⁄15 × x - 2⁄5 × 4⁄9 × x = 8
or, x = 8×31512=2108×31512=210
∴ Half of the number = 105
Answer D
Answer: D
Question: Divide Rs. 1200 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
Options:
A)s.800
B)s.400
C)s.600
D)s.500
E)s.300
Rationale: A+B+C = 1200
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1200 => 300
ANSWER:E
Answer: E
Question: If a(a + 5) = 6 and b(b + 5) = 6, where a ≠ b, then a + b =
Options:
A) −48
B) −5
C) 2
D) 46
E) 48
Rationale: a(a + 5) = 6
=> we have a = 1 or -6
also b(b + 2) = 6
=> b = 1 or -6
given a ≠ b
1) when a =1, b= -6 and a + b = -5
1) when a = -6, b= 1 and a + b = -5
Answer choice B
Answer: B
Question: The ratio 5 : 4 expressed as a percent equals
Options:
A)12.5%
B)40%
C)80%
D)125%
E)None
Rationale: Solution
5 : 4	= 5/ 4
= (5 / 4 x 100)%.
= 125 %.
Answer D
Answer: D
Question: Two trains start simultaneously from opposite ends of a 175-km route and travel toward each other on parallel tracks. Train X, traveling at a constant rate, completes the 175-km trip in 4 hours. Train Y, travelling at a constant rate, completes the 175-km trip in 3 hours. How many kilometers had Train X traveled when it met Train Y?
Options:
A)66
B)69
C)72
D)75
E)78
Rationale: If the two trains cover a total distance D, then Train X travels (3/7)*D while Train Y travels (4/7)*D. If the trains travel 175 km to the meeting point, then Train X travels (3/7)*175 = 75 km. The answer is D.
Answer: D
Question: If three distinct positive divisors of 128 are randomly selected, what is the probability that their sum will be less than 64?
Options:
A)1/3
B)3/7
C)5/14
D)9/28
E)21/56
Rationale: The positive divisors are 1, 2, 4, 8, 16, 32, 64, 128.
If any of the first six are chosen, the sum will be less than 64.
P(sum is less than 64) = 6/8 * 5/7 * 4/6 = 20/56 = 5/14
The answer is C.
Answer: C
Question: A train is running at a speed of 40 km/hr and it crosses a post in
18 seconds. What is the length of the train?
Options:
A)190 m
B)150 m
C)200 m
D)140 m
E)250 m
Rationale: speed = 40 km/hr = 40 * 5/18 = 100/9 m/s
time = 18 sec
distance covered = 100/9 * 18 = 200 m
so length of the train is = 200 m
ANSWER C
Answer: C
Question: Joseph’s grade was in the 80th percentile out of 100 grades in his class. In another class of 60 students there were 15 grades higher than Joseph’s. If nobody had Joseph’s grade, then Joseph’s was what percentile of the two classes combined?
Options:
A)80
B)78
C)75
D)60
E)90
Rationale: Being in 80% percentile out of 100 grades means Joseph was 81st (from the least grade) in the class (as long as nobody had Joseph’s grades), he outscored 80.
In another class his grade would rank him 46 (from the least grade out of 61, 60+Joseph), 45 had the grades lower than Amy.
So in combined classes he outscored 80+45=125. There are 160 students 125/160=0.78
Answer: B (78%)
Generally being in x% means that x% has the grades less than you.
Joseph in 80% --> he outscored 80% of of 100=80 (Joseph is 81st).
Of the 60 grades from another class, 15 were higher than Joseph 's, and the rest were lower --> rest is 45, hence Amy outscored 45.
So out of total 100+60=160, Joseph outscored 80+45=125. Hence he is in 125/160=78%.
Answer: B
Answer: B
Question: ramu sells gud for 27 per kg. but he has two plates for wighting one plate is 10% shorter then other.. he put 1 kg weight on shorter plat and apple on other plat.. at the end their is no profit no loss..what is cost price of apple
Options:
A)30
B)35
C)40
D)45
E)50
Rationale: ramu is making profit of 10% on weight because he puts 1 kg on shorter site.
to balance this profit if there is decrease of 1/10 in weight then there should be increse of 1/9 in price so 1/9 of 27=3
cost price=27+3=30
ans=30
ANSWER:A
Answer: A
Question: The number obtained by interchanging the two digits of a two-digit number is less than the original number by 45. If the sum of the two digits of the number so obtained is 13, then what is the original number?
Options:
A)49
B)94
C)83
D)38
E)48.5
Rationale: Let the number be in the form of 10a + b
Number formed by interchanging a and b = 10b + a.
a + b = 13 --- (1)
10b + a = 10a + b - 45
45 = 9a - 9b => a - b = 5 --- (2)
Adding (1) and (2), we get
2a = 18 => a = 9 and b = 4
The number is: 94.
ANSWER:B
Answer: B