divelab/Sys2Bench huggingface dataset:
Question: John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 10 minutes earlier. How far is the office from his house?
Options:
A)3 2/5 Km
B)3 3/5 Km
C)4 1/5 Km
D)5 1/5 Km
E)None
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 18/6
= 24/2 * 18/60
= 18/5 = 3 3/5 Km
B
Answer: B
Question: If Tim had lunch at $50.50 and he gave 30% tip, how much did he spend?
Options:
A)A)$57.45
B)B)$35.42
C)C)$65.65
D)D)$21.56
E)E)$78.45
Rationale: The tip is 30% of what he paid for lunch.
tip = 30% of 50.50 = (30/100)*50.50 = $15.15
Total spent
50.50 + 15.15 = $65.65
correct answer is C)$65.65
Answer: C
Question: Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4). What is the shape of the quadrilateral?
Options:
A)Square
B)Rectangle but not a square
C)Rhombus
D)Parallelogram but not a rhombus
E)Kite
Rationale: Explanatory Answer
The lengths of the four sides, AB, BC, CD and DA are all equal to 41−−√41. (Computation given in the last paragraph)
Hence, the given quadrilateral is either a Rhombus or a Square.
How to determine whether the quadrilateral is a square or a rhombus?
The diagonals of a square are equal. The diagonals of a rhombus are unequal.
Compute the lengths of the two diagonals AC and BD.
The length of AC is √162 and the length of BD is 2–√2.
As the diagonals are not equal and the sides are equal, the given quadrilateral is a Rhombus.
Choice C
Answer: C
Question: The events A and B are independent. The probability that event A occurs is m and the probability that event B occurs is n. Which of the following is equal to the probability that exactly one of the events A and B occurs?
Options:
A)m − 2mn
B)n − mn
C)m + n − 2mn
D)m + n − mn
E)m + n
Rationale: Probability of A occuring = m , Probability of A NOT occuring = 1-m
Probability of B occuring =n , Probability of B not occurring = 1-n
Probability of atleast of one of A and B occuring = 1-(1-m)(1-n) =m+n -mn
D
Answer: D
Question: Two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?
Options:
A)17
B)88
C)21
D)26
E)18
Rationale: Relative speed = 5.5 - 5 = .5 kmph (because they walk in the same direction)
distance = 8.5 km
time = distancespeed=8.5.5=17 hr
Answer :A
Answer: A
Question: A starts a business with a capital of Rs. 8500. B joins in the business with Rs.17000 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
Options:
A)2 months
B)6 months
C)7 months
D)8 months
E)None of these
Rationale: Explanation :
Let B joins for x months. Then
A:B = 8500*12 : x* 17000 = 3 : 1
=> 85*12 : 170x= 3 : 1
=> 85*12/ 170x = 3/1 = 3
=> 85*4 /170x = 1
=> 2/x = 1
=> x = 2. Answer : Option A
Answer: A
Question: If the wheel is 19 cm then the number of revolutions to cover a distance of 1156 cm is?
Options:
A)11
B)14
C)18
D)10
E)19
Rationale: 2 * 22/7 * 19 * x = 1156 => x = 9.7
Answer: D
Answer: D
Question: A photo-mat shop charges $0.40 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $24 if each film contains 36 photos?
Options:
A)2 films and 26 photos
B)5 films and 6 photos
C)5 films and 14 photos
D)6 films and 4 photos
E)6 films and 28 photos
Rationale: 1st photo = 0.4
Subsequent = 0.4*0.6=0.24
Price of 1 full film=0.4+0.24*35=8.8
Price of 2 full film = 8.8*2=17.6
24-17.6=6.4
6.4=0.4+0.24x
x=25
24--->2 full films and 1+25=26 photos
Answer: A
Answer: A
Question: If the consumer price index for a sample of goods and services purchased in Dallas rose from 100 at the end of 1967 to x at the end of 1985, what was the average W(arithmetic mean) annual increase in the index over this period?
Options:
A) (x + 100)/18
B) x/18
C) (100 − x)/18
D) (x − 100)/18
E) 100x/18
Rationale: CPI in end of 1967 = 100
CPI in end of 1985 = x
Number of years = 18
Average annual increase in CPI W= (x-100)/18
Answer D
Answer: D
Question: Mr. Smitherly leaves Cedar Rapids at 8:00 a.m. and drives north on the highway at an average speed of 50 km per hour. Mr. Dinkle leaves Cedar Rapids at 9:00 a.m. and drives north on the same highway at an average speed of 75 km per hour. Mr. Dinkle will
Options:
A)overtake Mr. Smitherly at 9:30 am
B)overtake Mr. Smitherly at 10:30 am
C)overtake Mr. Smitherly at 11:00 am
D)be 30 miles behind at 9:35 am
E)never overtake Mr. Smitherly
Rationale: After one hour, Mr. Smitherly is ahead by 50 km.
Mr. Dinkle gains on Mr. Smitherly 25 km each hour.
2 hours after 9:00 a.m., Mr. Dinkle will catch Mr. Smitherly.
The answer is C.
Answer: C
Question: A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in?
Options:
A)22
B)12
C)66
D)88
E)55
Rationale: Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/2
6/x = 1/2 => x = 12
So, B takes 6 hours to finish the work.
Answer: B
Answer: B
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x
Options:
A)1
B)2
C)34
D)12
E)13
Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
A
Answer: A
Question: 60% of the population of a village is 23040. The total population of the village is ?
Options:
A)38400
B)24000
C)24936
D)25640
E)None
Rationale: Answer
∵ 60% of P = 23040
∴ P = (23040 x 100) / 60 = 38400
Correct Option: A
Answer: A
Question: B is 8km East of A. C is 6km North of B. D is 12km East of C. E is 16km North of D. What is the distance b/w A and E.
Options:
A)20km
B)22km
C)18km
D)30km
E)33km
Rationale: it will make two rightangle triangles
1. 1st triangle ABC AB=8km & BC=6km.So AC=Squareroot(64+36)=10km.
2. 2nd triangle CDE CD=12km & DE=16km.So CE=Squareroot(144+256)=20km.
So, AC+CE = AE = 30km.
ANSWER:D
Answer: D
Question: If two numbers x, a perfect square and y, a perfect cube are added results a two digit number, whose digits if reversed, difference is 18, Find x and y ?
Options:
A)x=4,y=8
B)x=4,y=9
C)x=4,y=27
D)x=4,y=9
E)x=5,y=8
Rationale: 4+27=31
when reversed 13
31-13=18
x=4,y=27
ANSWER:C
Answer: C
Question: On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 360 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
Options:
A)237
B)287
C)197
D)287
E)720
Rationale: Explanation:
Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 360) = 2 + 2(extra)
=> 2x - 720 = x => x = 720.
Answer: E
Answer: E
Question: The length R of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?
Options:
A)Decreases by 19%
B)Decreases by 25%
C)Increases by 6%
D)Increases by 19%
E)Increases by 25%
Rationale: Let the length R of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy
Now after the change Length = 85x, and width = 140 y. Area = 11900xy
% Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D.
Answer: D
Question: A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
Options:
A)128228
B)12800
C)12819
D)12818
E)12812
Rationale: 16*8: x*4 = 5:2
x = 12.8 => Rs.12800
Answer: B
Answer: B
Question: Use distributive property to solve the problem below:
Maria bought 15 notebooks and 6 pens costing 2 dollars each.How much did Maria pay?
Options:
A)30 dollars
B)40 dollars
C)50 dollars
D)42 dollars
E)70 dollars
Rationale: Solution
2 × (15 + 6) = 2 × 15 + 2 × 6 = 30 + 12 = 42 dollars
Answer D
Answer: D
Question: The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
Options:
A)729
B)144
C)627
D)255
E)142
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 6 = 144.
Answer:B
Answer: B
Question: An express traveled at an average speed of 100 km/hr, stopping for 4 min after every 75 km. How long did it take to reach its destination 450 km from the starting point ?
Options:
A)8 hrs 29 min
B)4 hrs 50 min
C)2 hrs 28 min
D)6 hrs 28 min
E)1 hrs 28 min
Rationale: Explanation:
Time taken to cover 450 km = 450/100 = 4 hrs 30 mins
Number of stoppages = 450/75 - 1 = 5
Total time of stoppages = 4 x 5 = 20 min
Hence, total time taken = 4 hrs 50 min.
Answer: B
Answer: B
Question: The average age of man, women and their child 3 years ago was 27 years and that of women and the child 5 years ago was 20 years. The presentage of the man is?
Options:
A)35
B)37
C)40
D)41
E)56
Rationale: Sum of the present ages of man, women and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of women and child = (20 x 2 + 5 x 2) years = 50 years.
man's present age = (90 - 50) years = 40 years.
C
Answer: C
Question: Pointing to a person, a man said to a woman, "His mother is the only daughter of your father." How was the woman related to the person ?
Options:
A)Aunt
B)DAUGHTER
C)father
D)mother
E)sister
Rationale: Explanation:
Daughter of your father — Your sister. So, the person's mother is woman's sister or the woman is person's aunt.
Answer: A) Aunt
Answer: A
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 20% but the selling price
remains constant, approximately what percentage of the selling price is the profit
Options:
A)71%
B)81%
C)90%
D)100%
E)None of above
Rationale: Explanation:
Let C.P.= Rs. 100.
Then, Profit = Rs. 320,
S.P. = Rs. 420.
New C.P. = 120% of Rs. 100 = Rs. 120
New S.P. = Rs. 420.
Profit = Rs. (420 - 120) = Rs. 300
Required percentage = (300/420) * 100
= 71.40%(approx) =71%
Answer: A
Answer: A
Question: There are two sets A and B. The range of set A is 7, and the range of set B is 13. If the two sets are combined and get a new set E, which cannot be the range of the set E?
Options:
A)8
B)B.11
C)C.14
D)D.17
E)E.21
Rationale: Let Set A has 1,8 as elements
B has 1,14 as elements.. So Range for Combined set E becomes 14-1=13
For range to be 14,
A = 1,8
B= 2,15 (Range=14)
For range to be 17
A=1,8
B= 5,18
For range to be 21:
A=1,8
B= 9 ,22
So we are left with A and B.
Now consider A has elements A= -1,-8 and Thus Range =-1-(-8) =7
So for Range of combined set to be 11, B needs to have largest elementxso that x- (-8)=11 or x=3...But if x=3, the largest element in Combined Set then smallest element in the combined set will be 3-y=13 or y=-10....And the range of combined set 3-(-10)=13...
Consider Option A
A=-1,-8
B= y,x where y and x are smallest and largest element in Set B
Elements of Combined Set: -8,-1,y and x
Now x-(-8)=8 or x=0, then x-y=13 or y=-13...
Range of Combined Set: 0-(-13)= 13...
I don't see how range can be 8 or 11...Can you please post the source and explanation for the OA in spoiler...=B
Answer: B
Question: A large field of 700 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the average of the two areas. What is the area of the smaller part in hectares?
Options:
A)400
B)365
C)385
D)315
E)325
Rationale: Explanation:
Average of the two areas =7002=350
one-fifth of the average of the two areas=3505=70
⇒ Difference of the two areas =70
Let area of the smaller part =x hectares.
Then, area of the larger part =x+70 hectares.
x+(x+70)=700
⇒2x=630
⇒x=315
Answer: Option D
Answer: D
Question: If n is an integer and 101n^2 is less than or equal to 8100, what is the greatest possible value of n?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: 101 * n^2 <=8100
n^2 <=8100/101 which will be less than 81 since 8100/100 = 81 which is the square of 9
Next closest value of n where n^2<=81 is 8
Ans B
Answer: B
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
Options:
A)20%
B)28%
C)33 1/3 %
D)35 2/7 %
E)25%
Rationale: The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
ANSWER:C
Answer: C
Question: How many terms are there in 2,4,8,16……1024?
Options:
A)10
B)14
C)16
D)18
E)20
Rationale: Clearly 2,4,8,16……..1024 form a GP. With a=2 and r = 4/2 =2.
Let the number of terms be n . Then
2 x 2n-1 =1024 or 2n-1 =512 = 29.
n-1=9 or n=10.
ANSWER A 10
Answer: A
Question: What is the smallest integer k for which 64^k > 4^20?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: 64^k > 4^20
4^(3k) > 4^20
3k > 20
k = 7
The answer is D.
Answer: D
Question: Jake remembers only the last three letters of his four-letter Klingon name. If he is sure that the first letter is neither "N" nor "Z", and assuming that there are only 14 letters in the Klingon alphabet, what is the probability that he will give the correct name when asked for it by the space attendant?
Options:
A)A)1/12
B)B)9/100
C)C)1/8
D)D)4/5
E)E)9/10
Rationale: Total letters 14,out of which the first letter is anything of 10 but N or X...
So there are 12possible letters for first place..
And only one of them is correct..
So 1/12
Answer: A
Answer: A
Question: Working alone at its constant rate, machine K took 3 hours to produce 1/5 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?
Options:
A)10
B)12
C)15
D)25
E)30
Rationale: Machine K works at a rate of 1/15 of the units per hour.
The rate of K + M together is 4/5 * 1/6 = 2/15 of the units per hour.
The rate of machine M is 2/15 - 1/15 = 1/15.
It would have taken machine M a total time of 15 hours.
The answer is C.
Answer: C
Question: Pablo plays 3 rounds of a game, in which his chances of winning each round are 1/7, 1/2, and 1/n, respectively. If n ≠ 0, what is the probability that Pablo wins the first two rounds, but loses the third?
Options:
A)1/21n
B)(n-1)/14n
C)1/7n
D)(n+2)/72n
E)(3n-2)/2n
Rationale: 1/7 * 1/2 * (1-1/n)
= 1/14 * (n-1)/n
= (n-1)/14n
Answer - B
Answer: B
Question: A and B complete a work in 8 days. A alone can do it in 12 days. If both together can do the work in how many days?
Options:
A)4.8 days
B)3.8 days
C)3.65 days
D)3.77 days
E)5.75 days
Rationale: 1/8 + 1/12 = 5/24
24/5 = 4.8 days
Answer:A
Answer: A
Question: Aishwarya’s mom was 36 years of age at the time of her birth, while her mom was 30 years old when her 4 years younger sister was born. The variance between the parents ages is :
Options:
A)6 years
B)11 years
C)10 years
D)9 years
E)4 years
Rationale: C
10 years
Mom’s age when Aishwarya’s sister was born = 30 years.
Dad’s age when Aishwarya’s sister was born = (36 + 4) years = 40 years.
Needed Variance = (40 – 30) years = 10 years.
Answer is C
Answer: C
Question: A train running at the speed of 60 km/hr crosses a pole in 6 sec. What is the length of the train?
Options:
A)120 m
B)100 m
C)324 m
D)Cannot be determined
E)None of these
Rationale: Speed = 60* 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 6 = 100 m
ANSWER:B
Answer: B
Question: A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction T of the sum of the 21 numbers in the list?
Options:
A) 1/20
B) 1/6
C) 1/5
D) 4/21
E) 5/21
Rationale: This is how I used to calculate which I think works pretty well:
if you let the average of the 20 other numbers equal a, can you write this equation for sum of the list (S)
n + 20a = S
the question tells us that
n = 4a
plug this back into the first equation and you get that the sum is 24a
4a + 20a = 24a
therefore fraction T of n to the total would be
4a/24a or 1/6
answer B
Answer: B
Question: The difference between the compound interest and simple interest on a certain sum at 10% per annum for 2years is $631. Find the sum?
Options:
A)$52000
B)$61000
C)$71540
D)$63100
E)$56210
Rationale: Let the sum be $x
C.I. = x(1+10/100)^2 - x = 21x/100
S.I. = (X*10*2)/100 = X/5
C.I.- S.I. = (21x/100)-(x/5) = x/100
x/100 = 631
x = 63100
Answer is D
Answer: D
Question: Thrice the square of a natural number decreased by 4 times the number is equal to 50 more than the number. The number is:
Options:
A)4
B)5
C)6
D)7
E)10
Rationale: Let the number be x. Then,
3x2 - 4x = x + 50
3x2 - 5x - 50 = 0
(3x + 10)(x - 5) = 0
x = 5
ANSWER:B
Answer: B
Question: The length of a brigade which a train 130 m long and traveling at 45kmph can cross in 30 seconds, is
Options:
A)196 mts
B)220 mts
C)230 mts
D)245 mts
E)None of these
Rationale: Explanation:
Let the length of the brigade is x mts
Then Distance = 130 + x mts
given speed = 45 kmph = 45 x5/18 m/s
Time = 30 sec
T = D/S
=> 30 = 130+x/(45x5/18)
=> x = 245 mts.
ANSWER IS D
Answer: D
Question: A shopkeeper’s price is 50% above the cost price. If he allows his customer a discount of 30% what profit does he make?
Options:
A)5%
B)10%
C)15%
D)20%
E)None of these
Rationale: Let C.P. = 100, then M. P. = 150
S.P. = 70% of 150 = 105
∴ % profit = 105−100/100×100=5%
Answer A
Answer: A
Question: Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
Options:
A)6
B)5
C)6
D)3
E)2
Rationale: 9261 = 8000(21/20)N
(21/20)3 = (21/20)N => N = 3
Answer:D
Answer: D
Question: What is the least possible value of x^2-15 where x is a positive number.
Options:
A)-15
B)-14
C)-13
D)-12
E)-11
Rationale: If x is a positive integer, the lowest value would be x = 1, because 0 is not included in the natural numbers. That's a technicality the GMAT would not expect students to know.
If x = 1, then the expression equals -14.
Answer = (B).
Answer: B
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is ?
Options:
A)123 km/hr
B)187 km/hr
C)179 km/hr
D)120 km/hr
E)169 km/hr
Rationale: Let speed of the car be x km/hr.
Then, speed of the train = 150/100 x = 3/2 x km/hr.
75/x - 75/(3/2 x) = 125/(10 * 60)
75/x - 50/x = 5/24 = 120 km/hr.
Answer:D
Answer: D
Question: If a and y are positive integer and a/y is an even integer, which of the following can be an odd integer?
Options:
A)x
B)xy
C)x−y
D)x+2y
E)a/3
Rationale: C a-Y
Let says a =12 Y=3 iT BECOMES a-Y =9 This is odd True
a = 12 Y = 6 THEN a-Y = 2, Which is even hence this is False.
so both Yes and NO situations are exists for this Option. C can't be the correct answer same logic goes for E. I believe this question is incomplete b'coz of Irrelevant Options.
Answer: E
Question: If cost of 15 eggs be 75 rupees, then find out the cost of 4 dozen eggs.
Options:
A)300
B)240
C)500
D)600
E)700
Rationale: Cost of 15 eggs = 75 rupees
Cost of 1 egg = 75/15 = 5 rupees,
Cost of 4 dozens, i.e. 5 x 12 = 60 x 4 = 240
Answer : B
Answer: B
Question: Convert the 10/36 m/s into kilometers per hour?
Options:
A)2.9 kmph
B)9.9 kmph
C)1.3 kmph
D)1 kmph
E)5.7 kmph
Rationale: 10/36 m/s = 10/36 * 18/5 = 1/1
= 1kmph.
Answer: D
Answer: D
Question: Find the total no of 10 digits whose sum is 4.
Options:
A)210
B)220
C)230
D)240
E)250
Rationale: 4=4+0(one 4 & 9 zeroes)=> 1
4=3+1(one 3,one 1 & 8 zeroes)=> 2*9!/8!=18
4=2+2(two 2's & 8 zeroes)=> 9
4=1+1+2(two 1's & one 2)=> 9!/7! + 9!/(7!*2!)=72+36=108
4=1+1+1+1(four 1's)=> 9!/(6!*3!)=84
total no. of 10 digits no. whose sum is 4 =1+18+9+108+84=220
ans 220
ANSWER:B
Answer: B
Question: If 1.5 x= 0.04 y, then the value of (y-x) (y+x) is:
Options:
A)1405.25
B)1305.25
C)1205.25
D)1505.25
E)1605.25
Rationale: let us assume x=1 and y=37.5
then 1.5(x)=0.04(y)
that is 1.5(1)=0.04(37.5)
= 1.5 =1.5
therfore from given equation (37.5-1)(37.5+1)
=(36.5)(38.5)
=1405.25
ANSWER:A
Answer: A
Question: A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr. find the time taken by the boat to go 68 km downstream?
Options:
A)2 hours
B)3 hours
C)4 hours
D)5 hours
E)None
Rationale: Solution
Speed Downstream	= (13 + 4) km/hr
= 17 km/hr.
Time taken to travel 68 km downstream	=(68 / 17)hrs
= 4 hrs.
Answer C
Answer: C
Question: 9 men working 7 hours a day can complete a piece of work in 15 days. How many days can 6 men working for 9 hours a day, complete the same piece of work?
Options:
A)15 ¾ days
B)16 days
C)16 ¾ days
D)17 ½ days
E)18 days
Rationale: Explanation:
1 work done = 9 × 7 × 15
9 × 7 × 15 = 6 × 9 × ? days
? days = 9 × 7 × 15/6 × 9
= 35/2 = 17 ½ days.
Answer: Option D
Answer: D
Question: A biker covered half the distance between two towns in 2 hr 30 min. After that he increased his speed by 2 km/hr. He covered the second half of the distance in 2 hr 20 min. Find the distance between the two towns and the initial speed of the biker.
Options:
A)248
B)140
C)287
D)167
E)111
Rationale: Let x km/hr be the initial speed of the biker, then his speed during the second part of the trip is x + 2 km/hr. Half the distance between two cities equals 23060⋅x23060⋅x km and 22060⋅(x+2)22060⋅(x+2) km. From the equation: 23060⋅x=22060⋅(x+2)23060⋅x=22060⋅(x+2) we get x=28x=28 km/hr.
The intial speed of the biker is 28 km/h.
Half the distance between the two towns is
2h30min×28=2.5×28=702h30min×28=2.5×28=70.
So the distance is 2×70=1402×70=140 km.
Answer:B
Answer: B
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
Options:
A)1.9
B)1.5
C)1.1
D)1.3
E)1.2
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B
Answer: B
Question: The total surface area of a solid hemisphere of diameter 14 cm, is :
Options:
A)462 cm²
B)530 cm²
C)1345 cm²
D)1788 cm²
E)None
Rationale: Sol.
Total surface area = 3∏R² = [3 * 22/7 * 7 * 7] cm² = 462 cm²
Answer A
Answer: A
Question: Can you replace the question mark with the correct number, given the pair of numbers exhibits similar relationship?
? : 3839 :: 11 : 1209
Options:
A)6
B)16
C)26
D)36
E)46
Rationale: Formular used :
pow(x,3) - pow(x,2) - 1
11*11*11 - 11*11 - 1
1331 - 121 - 1
1209
Similarly, we can solve
pow($x,3) - pow($x,2) - 1 = 3839
This condition holds true for number-16.
correct answer is B)16
Answer: B
Question: If the S.P of Rs. 24 results in a 20% discount on the list price, What S.P would result in a 30% discount on the list price?
Options:
A)Rs. 27
B)Rs. 21
C)Rs.20
D)Rs. 9
E)Rs. 10
Rationale: Let the list price be Rs. X,
80/100*x = 24, x = 24*100/80 = 30
Required S.P = 70% of Rs. 30
= 70*30/100
=21
ANSWER:B
Answer: B
Question: What is 10-8+6-4+...+(-18)?
Options:
A) -8
B) 10
C) 12
D) -4
E) 16
Rationale: The expression considers all even numbers between 10 and -18 with alternate addition and subtraction of the numbers.
The numbers to be used are: 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10, -12, -14, -16, and -18.
Now, the first term is positive and the next term is subtracted. So, the required expression becomes,
10 - 8 + 6 - 4 + 2 - 0 + (-2) - (-4) + (-6) - (-8) + (-10) - (-12) + (-14) - (-16) + (-18)
= 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10 + 12 - 14 + 16 - 18
= 58 - 62
= -4
Hence the correct answer choice is D.
Answer: D
Question: In what ratio mental A at Rs.68 per kg be mixed with another metal at Rs.96 per kg so that cost of alloy (mixture) is Rs.76 per kg?
Options:
A)5:8
B)4:7
C)3:7
D)9:5
E)5:2
Rationale: (96-76)/(76-68)=20/8=5/2
ANSWER:E
Answer: E
Question: The sum of the non-prime numbers between 10 and 20, non-inclusive, is
Options:
A)60
B)75
C)90
D)105
E)120
Rationale: sum of consecutive integers from 11 to 19, inclusive ====> (A1 + An)/2 * # of terms = (11 + 19)/2 * 9 = 15 *9 = 135
sum of non-prime numbers b/w 10 and 20, non inclusive ===> 135 - 60 (i.e., 11 + 13 + 17 + 19, being the prime #s in the range) = 75
Answer: B
Answer: B