divelab/Sys2Bench huggingface dataset:
Question: When positive integer m is divided by positive integer x, the reminder is 7 and when positive integer n is divided by positive integer y, the reminder is 11. Which of the following R is a possible value for x + y?
I. 18
II. 19
III. 20
Options:
A)I only
B)II only
C)R=III only
D)II and III only
E)None
Rationale: TIP FOR SUCH QUESTIONS:Make Algebraic Equation in the beginning to understand how to proceed further. Then Start thinking the possible values of variables asked about
i.e.When positive integer m is divided by positive integer x, the reminder is 7can be understood as
m = ax +7which means thevalue of x must be greater than 7as the remainder 7 is possible only when the Divisor is bigger than the Remainder 7
i.e. Min Value of x = 8
AND
i.e.When positive integer n is divided by positive integer y, the reminder is 11can be understood as
n = by +11which means thevalue of y must be greater than 11as the remainder 11 is possible only when the Divisor is bigger than the Remainder 11
i.e. Min Value of y = 12
i.e. Minimum Value of x+y = 8+12 = 20
Hence III only can be True
Answer: Option
C
Answer: C
Question: In how many different number of ways 6 men and 2 women can sit on a shopa which can accommodate persons?
Options:
A)1680
B)1800
C)2000
D)2100
E)2300
Rationale: 8p4 = 8 Ã— 7 Ã— 6 x 5 = 1680
Answer :A
Answer: A
Question: At 6'o clock clock ticks 6 times. The time between first and last ticks was 30sec. How much time it takes at 8'o clock.
Options:
A)54sec
B)48sec
C)42sec
D)70sec
E)60sec
Rationale: At 6'0 clock, clock ticks 6 times.
So, there must be 5 intervals between clock ticks.
Time Between first and last ticks = 30sec
So, 1 interval = 30/5 = 6sec
So 6'o clock 5 *6=30sec
7'o clock 6 *6=36sec
8'o clock 7 *6=42sec
So, 42sec at 8'o clock.
ANSWER:C
Answer: C
Question: On a sum of money, the simple interest for 2 years is Rs. 327, while the compound interest is Rs. 340, the rate of interest being the same in both the cases. The rate of interest is
Options:
A)15%
B)14.25%
C)7.95%
D)10.5%
E)11.5%
Rationale: Explanation:
The difference between compound interest and simple interest on Rs. P for 2 years at R% per annum
= (R Ã— SI)/(2 Ã— 100)
Difference between the compound interest and simple interest = 340 - 327 = 13
(R Ã— SI)/(2 Ã— 100) = 13
(R Ã— 327)/(2 Ã— 100) = 13
R = 7.95%
Answer: Option C
Answer: C
Question: How is 1/2 % expressed as a decimal fraction?
Options:
A)0.5
B)0.05
C)0.005
D)0.0005
E)5
Rationale: as 1/2=0.5 and its percent value will be 0.5/100= 0.005
ANSWER:C
Answer: C
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize?
Options:
A)20
B)21
C)23
D)24
E)28
Rationale: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways
4: Or 4p = — 4:- 4X3X2X1- 24 ways
D
Answer: D
Question: A box contains six light out of which 3 are defective. If three light are chosen at random, find the probability that all the three light are defective?
Options:
A)2/25
B)3/20
C)1/30
D)3/35
E)None of these
Rationale: Out of nine light , five are good and four are defective.
Required probability = 3C3/6C3 = 1/20
B
Answer: B
Question: A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
Options:
A)Rs. 150
B)Rs. 144
C)Rs. 138
D)Rs. 132
E)None of these
Rationale: Given that SP = Rs. 102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.
To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = Rs. 144
ANSWER:B
Answer: B
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
Options:
A)277 m
B)776 m
C)500 m
D)187 m
E)1678 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.
Answer:C
Answer: C
Question: Mohan ranks twenty-first in a class of sixty-five students. What will be his (Mohan's)rank if the lowest candidate is assigned rank 1?
Options:
A)44th
B)45th
C)46th
D)Data inadequate
E)None of these
Rationale: 65=21+x-1
ans 45
ANSWER:B
Answer: B
Question: Two boys are standing side-by-side. One boy, which is 3 feets tall, casts a shadow that is 4.5
feets long. The other boy is 4 feets tall. Compute, in feets, the length of the shadow that
the taller boy casts.
Options:
A)8
B)10
C)6
D)4
E)12
Rationale: The ratio of shadow to height is constant, so if x is the length of the shadow, then
3/4.5 = 4/x and x = 6 .
correct answer C
Answer: C
Question: What proximate value should come in place of the question mark (?) in the following question?
6.795 Ã— 1084 + 2568.34 â€“ 1708.34 = ?
Options:
A)6,000
B)12,000
C)10,340
D)8,204
E)9,000
Rationale: ? â‰ˆ 6.8 Ã— 1080 + 2560 â€“ 1700 â‰ˆ 7344 + 860 â‰ˆ 8204
Answer D
Answer: D
Question: How much is 80% of 40 is greater than 4/5 of 25?
Options:
A)4
B)6
C)9
D)12
E)15
Rationale: Explanation:
(80/100) * 40 â€“ (4/5) * 25
32 - 20 = 12
ANSWER IS D
Answer: D
Question: If the area of circle is 1256 sq cm then its circumference?
Options:
A)125
B)135
C)140
D)110
E)145
Rationale: 22/7 r2 = 1256 => r =20
2 * 22/7 * 20 = 125
Answer: B
Answer: B
Question: The organizers of a week-long fair have hired exactly nine security guards to patrol the fairgrounds at night for the duration of the event. Exactly four guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different groups of 4 guards will be available to patrol the fairgrounds on the following Saturday night?
Options:
A)3
B)5
C)7
D)9
E)11
Rationale: For any given day, only the guards patrolling on the previous day won't be available. So, 4 guards who patrolled on Friday won't be available. We are thus left with 5 guards.
To choose 4 out of 5, we will have 5C4 = 5 different groups.
The answer is B.
Answer: B
Question: 10+45
Options:
A)8
B)55
C)87
D)90
E)2
Rationale: B
Answer: B
Question: A student is ranked 16th from right and 6th from left. How many students are there in totality ?
Options:
A)18
B)19
C)20
D)21
E)22
Rationale: From right 16 , From left 6
Total = 16+6-1 = 21
ANSWER:D
Answer: D
Question: The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is -.
Options:
A)(6!)2
B)6! * ⁷P₆
C)2(6!)
D)6! * 7
E)None of these
Rationale: We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.
Hence required number of ways = 6! * ⁷P₆
ANSWER:B
Answer: B
Question: In a village of 100 households, 85 have at least one DVD player, 90 have at least one cell phone, and 55 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x – y is:
Options:
A)65
B)55
C)45
D)35
E)25
Rationale: Am I missing something here??? it seems straightforward......
The obvious maximum that have all 3 is 55, because you are limited by the SMALLEST number.
The minimum is simply the sum of the max of each people who DONT have the product, so:
100-90 = 10 don't have Cell
100-85 = 15 don't have DVD
and 100-55 = 45 don't have MP3
SO a total of 10+15+45 = 70 combined who might NOT have SOME combination of the 3 products. So subtract that from 100, to give you the minimum of the people who COULD have all 3 and you get 100-70 = 30.
55-30 = 25
E
Answer: E
Question: A room of 8m 44cm long and 3m 50cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
Options:
A)73850
B)73805
C)844
D)350
E)2
Rationale: Explanation:
area of the room = 844 * 350 sq cm
size of largest square tile = H.C.F of 844cm and 350cm= 2cm
area of 1 tile = 2*2 sq cm
no. of tiles required = (844*350) / (2* 2) = 73850
Answer: A) 73850
Answer: A
Question: 2^8×39+31=?
Options:
A)34545
B)65657
C)65567
D)45677
E)56782
Rationale: 256*39+31
65567
C
Answer: C
Question: When x is divided by y, the quotient is p with remainder r. Which of the following is y in terms of r, x, and p? (Assume both y and p are nonzero.)
Options:
A)x – r – p
B)(x+r)/p
C)x/p−r
D)(x−r)/p
E)xr –p
Rationale: Given that when x is divided y, the quotient is p and remainder is r. This implies x-r is divisible by y and yp=(x-r) or y = (x-r)/p.
Answer D.
Answer: D
Question: In one hour, a boat goes 11 km along the steram and 5 km against the stream. The speed of the boat in still waer (in km/hr) is:
Options:
A)2
B)4
C)8
D)12
E)15
Rationale: Sol.
Speed in still water = 1/2 (11+5) kmph = 8 kmph.
Answer C
Answer: C
Question: A and B enter into a partnership with respective capitals of Rs. 20,000 and Rs. 40,000. At the end of the year, the total profit is Rs. 30,000. If A receives Rs. 15,000 as both his salary and profit, then what is his salary?
Options:
A)Rs. 2000
B)Rs. 4000
C)Rs. 5000
D)Rs. 3000
E)None of these
Rationale: Explanation:
A's capital : B 's capital
20000 : 40000 = 1 : 2
Since, the time period is fixed, the profit is distributed in the ratio of capital 1 : 2
Profit of A = (1/3) * 30,000 = Rs. 10,000
Salary of A = Rs. (15000 – 10000) = Rs. 5000
ANSWER: C
Answer: C
Question: Martha is 4 times the age of her daughter,Lyndra 4 years ago she was 8 times her daughters age,after how may years will martha be twice lyndra's age
Options:
A)14y
B)28y
C)7y
D)21y
E)22y
Rationale: Let m and l be the present ages of Martha and Lyndra
Then m=4l
4 years ago
(m-4)=8(l-4)
m = 8l-28
Equate "m"
4l = 8l - 28
4l = 28
l = 7
m = 28
After x years , Martha ll be twice of Lyndra
(m+x) = 2(l+x)
28+x = 2*7+2x
28+x = 14+2x
x = 14
So after 14 years martha and lyndra ages ll be 42 and 21
ANSWER:A
Answer: A
Question: Find the value of 201834 x 99999 = m?
Options:
A)20183198166
B)20194181766
C)20175292556
D)20132191166
E)20153198166
Rationale: 201834 x 99999 = 201834 x (100000 - 1)
= 201834 x 100000 - 201834 x 1
= 20183400000 - 201834
= 20183198166
A
Answer: A
Question: A man can row 3.3 km/hr in still water. It takes him twice as long to row upstream as to row downstream. What is the rate of the current ?
Options:
A)1.9
B)1.7
C)1.2
D)1.5
E)1.1
Rationale: Speed of boat in still water (b) = 3.3 km/hr. Speed of boat with stream (Down Stream), D = b + u Speed of boat against stream (Up stream), U = b – u It is given upstream time is twice to that of down stream. ⇒ Downstream speed is twice to that of upstream. So b + u = 2(b – u) ⇒ u =b/3 = 1.1 km/hr.
Answer: E
Answer: E
Question: The 80-milliliter solution of sugar and water is 20% sugar. How much water (in milliliters) must be added to make a solution that is 5% sugar?
Options:
A)240
B)280
C)320
D)360
E)400
Rationale: In the original solution the amount of sugar is 0.2*80=16 ml.
Let the volume of the new solution be V.
0.05V=16 ml.
V=320 ml.
The amount of water we need to add is 320 - 80 = 240 ml.
The answer is A.
Answer: A
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 24 hours and 8 hours respectively. The ratio of their speeds is
Options:
A)4 : 9
B)4 : 3
C)1 : 3
D)4 : 8
E)4 : 5
Rationale: Let us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 8 : 24 = 1 : 3.Answer: C
Answer: C
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
Options:
A)22 Kmph
B)68 Kmph
C)56 Kmph
D)11 Kmph
E)76 Kmph
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer: B
Answer: B
Question: An aeroplane covers a certain distance of 450 Kmph in 4 hours. to cover the same distance in 3 2/3 hours, it Must travel at a speed of
Options:
A)440
B)490
C)640
D)740
E)250
Rationale: Speed of aeroplane = 450 Kmph
Distance travelled in 4 hours
= 450 * 4 = 1800 Km
Speed of aeroplane to acver 1800 Km in 11/3
= 1800*3/11 = 490 Km
Answer B.
Answer: B
Question: Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?
Options:
A)10.49
B)10.4
C)10.42
D)10.41
E)10.46
Rationale: S.I. on Rs. (260 - 20) for a given time = Rs. 20.
S.I. on Rs. 240 for half the time = Rs. 10.
T.D. on Rs. 250 = Rs. 10.
T.D. on Rs. 260 = Rs. 10	x 260 = Rs. 10.40
250
Answer: B
Answer: B
Question: A train 300 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options:
A)987
B)54
C)72
D)27
E)28
Rationale: Length = Speed * time
Speed = L/T
S = 300/20
S = 15M/Sec
Speed= 15*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 54Kmph
Answer:B
Answer: B
Question: X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 43 Km/hr. However, he covers the distance from Y to X at an average speed of 34 Km/hr. His average speed during the whole journey in km/hr. is :
Options:
A)34
B)43
C)40
D)38
E)29
Rationale: Solution: Average speed = 2XY / X+Y
= 2*43*34 / 43+34
= 2924 / 77
= 37.974... = 38
Answer : D
Answer: D
Question: Preeti covers a distance in 40 min , if she drives at a speed of 60 km/h on an average. Find the speed at which she must drive at to reduce the time of the journey by 50%.
Options:
A)60 km/h
B)70 km/h
C)117.64 km/h
D)100 km/h
E)125.25 km/h
Rationale: Given Speed = 60 Kmph.
It means Preeti covered 60 km in 60 min (1 hour). So, in 40 min he will cover 40 km.
50% time reduced = 40 - 50% of 40 = 20 min.
Thus, Preeti needs to cover 40 km in 20 min (0.34 hour).
Speed * Time = Distance.
Speed * 0.34 = 40
Speed = 117.64 kmph.
ANSWER : OPTION C
Answer: C
Question: If a boat is rowed downstream for 600 km in 20 hours and upstream for 48 km in 4 hours, what is the speed of the boat and the river?
Options:
A)21 , 21
B)9 , 21
C)21 , 9
D)9 , 9
E)20 , 8
Rationale: Explanation:
If x: speed of boats man in still water
y: speed of the river
Downstream speed (Ds) = x + y
Upstream speed (Us) = x â€“ y
x = (Ds + Us) / 2
y = (Ds â€“ Us) / 2
In the above problem Ds = 30 ; Us = 12
x = (30 + 12) / 2 = 42/2 = 21 km/hr
y = (30 - 12)/2 = 18/2 = 9 km/hr
ANSWER: C
Answer: C
Question: If a, b and c are forming increasing terms of G.P., r is the common ratio then find the minimum value of (c-b), given that (log a+log b+log c)/log 6 = 6.Note that r can be any real no.
Options:
A)23
B)16
C)17
D)12
E)62
Rationale: Explanation:
a,b,c are in G.P. so let the first term of G.P. = arar, and common ratio = r.
Therefore, a = arar, b = aa, c = arar
Given, loga+logb+logclog6=6log⁡a+log⁡b+log⁡clog⁡6=6
⇒logabclog6=6⇒log⁡abclog⁡6=6
⇒log6abc=6⇒abc=66⇒log6abc=6⇒abc=66
put the value of a,b,c in gp format
⇒ar×a×ar=66⇒ar×a×ar=66
⇒a3=66⇒a=36⇒a3=66⇒a=36
Now a = 36r36r, b = 36, c = 36r.
We have to find the minimum value of c - b = 36r - 36.
r can be any number. So for r < 0, we get c - b negative.
When r = 1, c - b = 0
But none of the options are not representing it.
From the given options, r = 4/3, then c = 48. So option d satisfies this.
Answer: D
Answer: D
Question: One fourth of a solution that was 22% sugar by weight was replaced by a second solution resulting in a solution that was 35 percent sugar by weight. The second solution was what percent sugar by weight?
Options:
A)74%
B)24%
C)22%
D)18%
E)8.5%
Rationale: Say the second solution (which was 1/4 th of total) was x% sugar, then 3/4*0.22+1/4*x=1*0.35 --> x=0.74. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.22+25*x=100*0.35 --> x=0.74.
Answer: A.
Answer: A
Question: Working alone, Mary can pave a driveway in 5 hours and Hillary can pave the same driveway in 3 hours. When they work together, Mary thrives on teamwork so her rate increases by 10%, but Hillary becomes distracted and her rate decreases by 10%. If they both work together, how many hours will it take to pave the driveway?
Options:
A)2 hours
B)4 hours
C)5 hours
D)6 hours
E)7 hours
Rationale: Initial working rates:
Mary = 1/5 per hour
Hillary = 1/3 per hour
Rate when working together:
Mary = 1/5 + (1/10*1/5) = 2/9 per hour
Hillary = 1/3 - (1/10*1/3) = 3/10 per hour
Together they work 2/9 + 3/10 = 1/2 per hour
So they will need 2 hours to complete the driveway. The correct answer is A.
Answer: A
Question: A and B together can do a piece of work in 1 days. If A alone can do the same work in 20days, then B alone can do the same work in?
Options:
A)0.35 days
B)0.45 days
C)0.55 days
D)0.25 days
E)0.95 days
Rationale: B = 1/1 – 1/20 =0.95 days
ANSWER:E
Answer: E
Question: Which of the following is a divisible by 9 number ?
Options:
A)91
B)81
C)78
D)22
E)11
Rationale: Explanation :
81 is a divisible by 9
Answer : Option B
Answer: B
Question: In a classroom, if 6 students per bench are assigned to accommodate all students, one more bench will be required. However, if 7 students are accommodate per bench, there would be a space left for 5 students.What is the number of students in the class ?
Options:
A)30
B)45
C)42
D)72
E)75
Rationale: Let the number of benches in the class be x.
Then, 6(x + 1) = 7x - 5
x = 11.
Hence, number of students in the class	= 6 ( x + 1)
= 6 x 12
= 72.
ANSWER:D
Answer: D
Question: 75 boys can complete a job in 24 days. How many men need to complete the job twice in 20 days
Options:
A)160
B)170
C)180
D)190
E)200
Rationale: One man can complete the job in 24*75=1800 days
To complete the job twice he would need 3600 days.
Thus, to complete the job in 20 days, 3600/20=180 men are needed.
ANSWER:C
Answer: C
Question: In a room there are 10 people. Each shake hands with every other person. How many hand shakes?
Options:
A)50
B)62
C)75
D)45
E)61
Rationale: Any pair of person = 10C2 = 10!/8!*2! = 45
Answer is D
Answer: D
Question: Consider four consecutive integers. What is the sum of the 2nd and fourth numbers if the first number is 13?
Options:
A)26
B)19
C)30
D)43
E)None
Rationale: 1st = x = 13
2nd = x+1
3rd = x+2
4th = x+3
------
sum of 2nd and fourth numbers::
x+1+x+3 = 13+1+13+3 = 30
Answer C
Answer: C
Question: The ratio of the incomes of Chetan and Dinesh is 3:4. The ratio of their expenditures is 5:7. If each of them saves Rs.200, find the incomes of both?
Options:
A)Rs.1200,Rs.1800
B)Rs.1200,Rs.1000
C)Rs.8200,Rs.1600
D)Rs.1200,Rs.1960
E)Rs.1200,Rs.1600
Rationale: The savings of Chetan and Dinesh are 3x - 5y and 4x - 7y respectively.
3x - 5y = 200 --- (1)
4x - 7y = 200 --- (2)
Multiplying (1) by 7 and (2) by 5 and subtracting the resultant equation (2) from resultant equation (1), we get x = 400.
The incomes of Chetan and Dinesh are 3x = Rs.1200 and 4x = Rs.1600 respectively.
Answer:E
Answer: E
Question: The average of first 12 natural numbers is?
Options:
A)5.2
B)6.5
C)5.3
D)5.9
E)5.1
Rationale: Sum of 12 natural no. = 156/2 = 78
Average = 78/12 = 6.5
Answer:B
Answer: B
Question: A man can do a job in 15 days. His father takes 20 days and his son finishes it in 15 days. How long will they take to complete the job if they all work together?
Options:
A)6.3
B)6.9
C)5.5
D)6.1
E)6.2
Rationale: 1 day work of the three persons = (1/15 + 1/20 + 1/15) = 11/60
So, all three together will complete the work in 300/47 = 5.5 days.
Answer:C
Answer: C
Question: On Sunday, Bill ran 4 more miles than he ran on Saturday. Julia did not run on Saturday, but she ran twice the number of miles on Sunday that Bill ran on Sunday. If Bill and Julia ran a total of 28 miles on Saturday and Sunday, how many miles did Bill run on Sunday?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Let Bill run x on saturday, so he will run x+4 on sunday..
Julia will run 2*(x+4) on sunday..
totai= x+x+4+2x+8=28..
4x+12=28..
x=4..
ans =x+4=4+4=8
Aswer D
Answer: D
Question: A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
Options:
A)1079
B)1017
C)1023
D)1017
E)1012
Rationale: Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.
Hence, the required number of ways = 45 - 1.
= 210 - 1 = 1024 - 1 = 1023
Answer: C
Answer: C
Question: Mike took 5 mock tests before appearing for the GMAT. In each mock test he scored 5 points more than the previous mock test. If he scored 760 on the GMAT and his average score for the mocks and the GMAT was 726.67, what was the difference in the score of his last mock and his GMAT score?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: One way to do this would be weighted average method..
1) let the average of 5 mocks be x...
so take it as a mix of5 quantitites of xand1 quantity of 760resulting in an average of 726.67...
By alligation/weighted average..
the difference in 760 and 726.67 is 5/6 of difference of 760 and x..
760-726.67 = 5/6 * (760-x)
760-x= 33.33*6/5=40...
so x = 720..
the last of mock test will be 720+5+5=730...
so ans = 760-730=30
B
Answer: B
Question: Set D consists of all the prime numbers between 10 and 25. What is the range of set D?
Options:
A)12
B)13
C)16.6
D)17
E)23
Rationale: Answer of set D is 12=A
Answer: A
Question: On a Monday in a certain restaurant, 20 percent of the 170 customers ordered the daily special. On Tuesday, only 10 percent of the 120 customers ordered the special. For the two days combined, what percent of the customers ordered the daily special?
Options:
A)15%
B)16%
C)18%
D)23%
E)30%
Rationale: 20% of 170= 34
10% of 120=12
Total =46
percent for 2 days combined =46/300 ≈0.15. so it should be less than 0.15 so it is 15%
Answer:A
Answer: A
Question: How many integers n are there such that 1< 4n +4 < 20?
Options:
A) Five
B) Four
C) Three
D) Two
E) One
Rationale: Solution:
1< 4n + 4 < 20
1< 4n + 4 < 20
We first subtract 4 from all three parts of the inequality, and we obtain:
-3 < 4n < 16
Next, we divide both sides of the inequality by 4 and we get:
-3/4 < n < 4
The answer is B
Answer: B
Question: A seller uses 800gm in place of 1kg to sell his goods. Find his actual % profit or loss, when he sells his article his article on 10% gain on cost price?
Options:
A)32.5%
B)37.5%
C)35%
D)40%
E)50%
Rationale: Selling price of 800gm = 100+10 = $110
Profit = 110-80 = $30
% of profit = 30*100/80 =37.5 %
Answer is B
Answer: B
Question: A man sitting in a train which is traveling at 60 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?
Options:
A)52 kmph
B)58 kmph
C)62 kmph
D)65 kmph
E)75 kmph
Rationale: Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph.
Speed of goods train = (112 - 60) kmph = 52 kmph.
Answer : A
Answer: A
Question: Zeynep (the lady of the rings) has 10 identical gold, 10 identical silver and 10 identical bronze rings. (total of 30) She always wears exactly 3 rings on each of her 10 fingers in a particular sequence: first gold, then silver and last bronze. In how many different orders can she wear her 30 rings?
Options:
A)(10!)^3 / 2^10
B)(10!)^3 / 3^10
C)30! / 2^10
D)30! / 3^10
E)30! / 6^10﻿
Rationale: By convention, the answer choice letters are typically listed as capital letters, not lower case. Also, professional math notation is always preferable to plain text shortcuts.
30! / 6^10﻿
ANSWER:E
Answer: E
Question: The circumferences of two circles are 396 meters and 704 meters. Find the difference between the areas of the larger and the smaller circles?
Options:
A)29960 sq m
B)26950 sq m
C)43120 sq m
D)27680 sq m
E)27786 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 396 and 2∏l = 704
s = 396/2∏ and l = 704/2∏
Difference between the areas = ∏l^2 - ∏s^2
= ∏{198^2/∏^2 - 352^2/∏^2}
= 198^2/∏ - 352^2/∏
= (198 - 352)(198 + 352)/∏
= (154)(550)/(22/7)
=26950 sq m
Answer:B
Answer: B