divelab/Sys2Bench huggingface dataset:
Question: How many four-digit numbers that do not contain the digits 2, 3, or 6 are there?
Options:
A)2058
B)3584
C)4096
D)5040
E)7200
Rationale: The 1st digit can be filled up by the numbers: {1,4,5,7,8,9} = 6 ways
The 2nd digit can be filled up by the numbers: {0,1,4,5,7,8,9} = 7 ways
The 3rd digit can be filled up by the numbers: {0,1,4,5,7,8,9} = 7 ways
The 4th digit can be filled up by the numbers: {0,1,4,5,7,8,9} = 7 ways
The total number of such four-digit numbers is 6*7*7*7 = 2058
The answer is A.
Answer: A
Question: All of the citizens of a country have a seven-character or eight-character national identification code that is created using the 26 letters of the alphabet and the 10 digits from 0 to 9. What is the maximum number of citizens who can be designated with these codes?
Options:
A)36^15
B)35(36^7)
C)35(36^8)
D)37(36^7)
E)37(36^8)
Rationale: The number of possible 7-digit codes is 36^7.
The number of possible 8-digit codes is 36^8.
The total sum is 36^7 + 36^8 = 36^7(1+36) = 37(36^7)
The answer is D.
Answer: D
Question: A girl swims downstream 112 km and upstream 32 km taking 8 hours each time, what is the speed of the girl in still water?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: 112 --- 8 DS = 14
? ---- 1
32 ---- 8 US = 4
? ---- 1 M = ?
M = (14 + 4)/2 = 9
Answer:B
Answer: B
Question: A train 125 m long crosses a platform 125 m long in 14 sec; find the speed of the train?
Options:
A)87 kmph
B)64 kmph
C)54 kmph
D)16 kmph
E)18 kmph
Rationale: D = 125 + 125 = 250
T = 14
S = 250/14 * 18/5 = 64 kmph
Answer:B
Answer: B
Question: Last year, the price of a vacation package was P. At the beginning of this year, the price went up 30%. Lucas used a travel voucher to purchase the vacation package at 20% off this year’s price. In terms of P, how much did Lucas pay?
Options:
A) P + 10
B) 1.1*P
C) 1.12*P
D) 0.04*P
E) 1.04*P
Rationale: Last year price = P;
This year price = 1.3P;
Lucas used a travel voucher to purchase the vacation package at 20% off this year’s price, thus he paid (1 - 0.2)*1.3P = 1.04P.
Answer: E.
Answer: E
Question: The largest four-digit number which when divided by 4, 7 or 13 leaves a remainder of 3 in each case,is :
Options:
A)8739
B)9831
C)9834
D)9893
E)8976
Rationale: Solution
Greatest number of 4 digits is 9999. L.C.M. of 4, 7, and 13 = 364.
on dividing 9999 by 364, remainder obtained is 171.
So, greatest number of 4 digits divisible by 4,7, and 13 = (9999 - 171) = 9828.
Hence, required number = (9828 + 3) = 9831.Answer B
Answer: B
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.50000?
Options:
A)6620
B)3277
C)16550
D)2998
E)2789
Rationale: A = 50000(11/10)3
= 66550
= 50000
----------
16550
Answer:C
Answer: C
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
Options:
A)6
B)9
C)8
D)2
E)1
Rationale: Explanation:
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
{\color{Black} \therefore } 14 : 6 :: 21 : x {\color{Black} \Rightarrow } 14 x x = 6 x 21
x={\color{Black} \frac{6\times 21}{14} } {\color{Black} \Rightarrow } x=9
Answer: B) 9
Answer: B
Question: If the average (arithmetic mean) of a and b is 120, and the average of b and c is 150, what is the value of a − c?
Options:
A)−60
B)−100
C)100
D)135
E)It cannot be determined from the information given
Rationale: a+b = 240
b+c = 300
a-c = -60.
IMO option A.
Answer: A
Question: Which one of the following is not a prime number?
Options:
A)31
B)61
C)71
D)91
E)98
Rationale: 91 is divisible by 7. So, it is not a prime number.
Answer: Option D
Answer: D
Question: A builder purchased a plot of land for 80 lakh and constructed a five-storey building inclusive of ground floor on it. How much should he charge for each flat to make 25% profit on his investment on land, if there are five flats on each storey?
Options:
A)50000
B)100000
C)500000
D)2000000
E)None of these
Rationale: We do not know the total investment of builder,because in the question construction cost is not given.
Hence,‘None of these’ is the answer.
Answer E
Answer: E
Question: A person can swim in still water at 10 km/h. If the speed of water 8 km/h, how many hours will the man take to swim back against the current for 16km?
Options:
A)3
B)7
C)5
D)8
E)6
Rationale: M = 10
S = 8
US = 10 - 8 = 2
D = 16
T = 16/2 = 8
Answer: D
Answer: D
Question: A polling company reports that there is a 40% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z?
Options:
A)10
B)8
C)6
D)4
E)5
Rationale: Fairly straight forward...
40% - Candidate Elected
100%-60% = 40% - Candidate does not sigh Bill X
50% - Candidate randomly chooses between two bills.
These are multiplicative:
40% x 40% x 50%
0.4 x 0.4 x 0.5 = 0.08 = 8%
Answer (B)
Answer: B
Question: electric running buzzer rang after every 60 sec.and second buzzer rang after every 62 sec.both rung together at 10'o clock.after that at what time both rang together?
Options:
A)morning 10:30
B)morning 10:31
C)morning 10:59
D)morning 11:00
E)none of these
Rationale: difference of time between together ringing of buzzer=l.c.m of 60 sec. and 62 sec.
(2*30*31) sec.={2*30*31}/60=31 minute
hence,next time they rang together at morning 10:31
answer B
Answer: B
Question: If both 7^2 and 3^3 are factors of the number a*4^3*6^2*13^11, then what is the smallest possible value of a?
Options:
A)99
B)147
C)363
D)1200
E)1625
Rationale: The number a must include at least 3*7^2 = 147
The answer is B.
Answer: B
Question: Life expectancy is defined by the formula 2SB/G, where S = shoe size, B = average monthly electric bill in dollars, and G = GMAT score. If Melvin's GMAT score is twice his monthly electric bill, and his life expectancy is 100, what is his shoe size?
Options:
A)100
B)55
C)85
D)40
E)50
Rationale: Solution -
Given that, G = 2B and Life expectancy(L) = 100
L=2SB/G -> 100 = 2SB/2B --> S=100.
ANS A
Answer: A
Question: Of the 300 math majors at a certain university, 30 percent will be assigned to advanced calculus on Monday and Wednesday and the remaining 70 percent will be assigned to advanced calculus on Tuesday and Thursday. However, 40 percent of the math majors prefer Tuesday and Thursday and 60 percent prefer Monday and Wednesday. What is the lowest possible number of math majors who will NOT be assigned to the days they prefer?
Options:
A) 15
B) 20
C) 30
D) 45
E) 60
Rationale: 30% of students are assigned to Monday and Wednesday = 0.3*200 = 60
70% of students are assigned to Tuesday and Thursday = 0.7*200 = 140
60% of students prefer Monday and Wednesday = 0.6*200 = 120
40% of students prefer Tuesday and Thursday = 0.4*200 = 80
Since we need theleastnumber of students who will not be assigned to their preferred days, we shall fit in themaximumpossible students as per their preference:
All of the 40% of students who prefer Tuesday and Thursday can be accommodated to their preferred days, whereas only 60 out of 120 students who prefer Monday and Wednesday can be accommodated to their preferred days.
The remaining 30 students who prefer Monday and Wednesday will be allocated to Tuesday and Thursday by default, which is not their choice.
Answer is C.
Answer: C
Question: Given that 1 + 3x > 4 and 2x - 3 < 5, all values of x must be between which of the following pairs of integers?
Options:
A)3 and 8
B)1 and 4
C)3 and 12
D)4/3 and 5/2
E)-5 and 1
Rationale: Given, 1 + 3x > 4 and 2x - 3 < 5
i.e. 3x > 3 and 2x < 8
i.e. x > 1 and x < 4
Answer: Option B
Answer: B
Question: Find the odd man out
1, 2, 6, 24, 120, 620
Options:
A)2
B)620
C)120
D)24
E)6
Rationale: 1.1 =1
1*2 =2
2*3 =6
6*4 =24
24*5=120
120*6=720
ANSWER:B
Answer: B
Question: 5216 x 51 = ?
Options:
A)266016
B)212016
C)266436
D)216314
E)None of these
Rationale: Explanation :
Normal way of multiplication may take time. Here are one alternative.
5216 x 51 = (5216 x 50) + 5216 = (5216 x 100/2) + 5216
= 521600/2 + 5216 = 260800 + 5216 = 266016. Answer : Option A
Answer: A
Question: A cycle is bought for Rs.900 and sold for Rs.1120, find the gain percent?
Options:
A)11
B)24
C)99
D)77
E)18
Rationale: 900 ---- 220
100 ---- ? => 24%
Answer: B
Answer: B
Question: Which of the following integers can be written as both the sum of 5 consecutive odd integers and 7 consecutive odd integers?
Options:
A)49
B)70
C)140
D)215
E)525
Rationale: First of all notice that both the sum of 5 consecutive odd integers and the sum of 7 consecutive odd integers must be odd. Eliminate B, and C right away.
Next the sum of 5 consecutive odd integers can be written as: (x-4)+(x-2)+x+(x+2)+(x+4)=5x, so the sum must be odd multiple of 5;
Similarly, the sum of 7 consecutive odd integers can be written as: (y-6)+(y-4)+(y-2)+y+(y+2)+(y+4)+(y+6)=7y, so the sum must be odd multiple of 7;
So, the sum must be odd multiple of 5*7=35. Only option E this conditions.
Answer: E.
Answer: E
Question: A & B are two towns. A person covers the distance from A to B on cycle at 17kmph and returns to A by a boat running at a uniform speed of 8kmph. His average speed for the whole journey is
Options:
A)09.88kmph
B)12.88kmph
C)10.88kmph
D)16.45kmph
E)13.71kmph
Rationale: C
10.88kmph
When same distance is covered with different speeds, then the average speed = 2xy / x+y = 10.88kmph
Answer: C
Question: The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
Options:
A)23.9 cm
B)62.9 cm
C)91.5 cm
D)26.8 cm
E)16.8 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42
= 91.5 cm
Answer:C
Answer: C
Question: A right triangle ABC has to be constructed in the xy-plane so that the right angle is at A and AB is parallel to x axis. The coordinates of A, B and C are to satisfy the inequalities -3 ≤ x ≤ 5 and 2 ≤ y ≤11 and x and y are integers. The number of different triangles that can be constructed with these properties are?
Options:
A)100
B)6480
C)2320
D)1500
E)9000
Rationale: We have the rectangle with dimensions 9*10 (9 horizontal dots and 10 vertical). AB is parallel to x-axis and AC is parallel to y-axis.
Choose the (x,y) coordinates for vertex A: 9C1*10C1=90;
Choose the x coordinate for vertex B (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);
Choose the y coordinate for vertex C (as x coordinate is fixed by A): 9C1, (10-1=9 as 1 vertical dot is already occupied by A).
9C1*10C1*8C1*9C1=6480.
Answer: B.
Answer: B
Question: Solution Y is 30 percent liquid X and 70 percent water. If 4 kilograms of water evaporate from 8 kilograms of solution Y and 4 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X?
Options:
A)40%
B)41 1/2%
C)44%
D)45%
E)46%
Rationale: In 8 kilograms of solution Y there are 0.3*8=2.4 kilograms of solution X;
After 4 kilograms of water are replaced by 4 kilograms of solution Y, to the existing 2.4 kilograms of solution X, 0.3*4=1.2 kilograms of solution X are added, so in the new solution of 8 kilograms there are 2.4+1.2=3.6 kilograms of solution X, which is 3.6/8*100=45% of this new solution.
Answer: D.
Answer: D
Question: A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?
Options:
A)1
B)2
C)3
D)4
E)65
Rationale: SP of first article = 1000
Profit = 20%
CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3
SP of second article = 1000
Loss = 20%
CP = (SP)*[100/(100-L)] = 5000/4 = 1250
Total SP = 2000
Total CP = 2500/3 + 1250 = 6250/3
CP is more than SP, he makes a loss.
Loss = CP-SP = (6250/3)- 2000 = 250/3
Loss Percent = [(250/3)/(6250/3)]*100
=0.04 * 100 = 4%
Answer: D
Answer: D
Question: If the area of a circle decreases by 20%, then the radius of a circle decreases by
Options:
A)20%
B)18%
C)36%
D)11%
E)None of these
Rationale: If area of a circle decreased by x % then the radius of a circle decreases by
(100−10√100−x)%=(100−10√100−20)%
= (100−10√80)%
= 100 - 89 = 11%
Answer D
Answer: D
Question: A man can hit the target once in four shots. If he fires five shots in succession, what is the probability that he will hit the target?
Options:
A)1
B)1/256
C)81/59
D)45/59
E)185/59
Rationale: In five shots he can hit once,twice,thrice,four, all hit
the probability of hitting the target is p(1hit out of 5)+P(2hit out of 5)+p(3hit out of 5)+p(4hit out of 5)+p(All hit)
it is total probability-probability of not hitting the target
=>1-(3/4*3/4*3/4*3/4*3/4)
=>45/59
ANSWER:D
Answer: D
Question: Which of the following MUST yield an integer when divided by 9?
Options:
A)The sum of nine consecutive positive integers.
B)The square of a prime number.
C)The sum of two odd integers.
D)The product of three consecutive odd numbers.
E)The difference between a multiple of 8 and a multiple of 3.
Rationale: For option A: Let the numbers be (x-4), (x-3), (x-2), (x-1), (x), (x+1), (x+2), (x+3), (x+4).
Now, (x-4)+(x-3)+(x-2)+(x-1) + (x) + (x+1) + (x+2)+(x+3)+(x+4) = 9(x). Hence A is true. No need to check other answers since there can only be one correct answer.
So, Ans(A)
Answer: A
Question: The area of a field in the shape of a trapezium measures 1440sq m. The perpendicular distance between its parallel sides is 24cm. If the ratio of the sides is 5:3, the length of the longer parallel side is:
Options:
A)75
B)25
C)26
D)76
E)19
Rationale: Explanation:
Area of field = = 96x sq.m
96x = 1440 x = = 15
Hence, the length of longer parallel side = 5x = 75m
Answer: A) 75
Answer: A
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
Options:
A)234
B)3444
C)3333
D)4082.4
E)23468
Rationale: Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40
Answer: Option D
Answer: D
Question: A number consisting of five digits 5,6,7,8 and 9 each coming once but
not necessarily in that order is taken ,and an algorithm specified in the
previous question is run on it .How many different end results are possible
?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: 5+6+7+8+9=35
3+5=8..only one result possible!
ANSWER:A
Answer: A
Question: 900 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
Options:
A)162
B)18
C)60
D)38
E)12
Rationale: Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 900 = 18
Answer: B
Answer: B
Question: Two pipes A and B can fill a tank in 15 min and 18 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?
Options:
A)14 min 19 sec
B)13 min 36 sec
C)14 min 20 sec
D)14 min 40 sec
E)14 min 10 sec
Rationale: :
Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15
Remaining part = 1 - 7/15 = 8/15
Part filled by B in 1 minute = 1/18
1/18 : 8/15 :: 1 ; x
x = 8/15 * 1 * 18 = 9 3/5 min = 9 min 36 sec.
The tank will be full in (4 min. + 9 min. 36 sec) = 13 min 36 sec.Answer: B
Answer: B
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 12 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Options:
A)76 km/hr
B)66 km/hr
C)40 km/hr
D)67 km/hr
E)22 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/12 = 3x => x = 50/9
So, speed of the faster train = 100/9 = 100/9 * 18/5 = 40 km/hr.
Answer:C
Answer: C
Question: In the figure given below, ABC and CDE are two identical semi-circles of radius 2 units. B and D are the mid points of the arc ABC and CDE respectively. What is the area of the shaded region?
Options:
A)4π - 1
B)3π - 1
C)2π - 4
D)½(3π - 1)
E)2π - 2
Rationale: Solution
P and Q are the centers of the two semicircles.
Draw BP perpendicular to AC.
BP is radius to the semi-circle. So are AP and PC.
Therefore, BP = AP = PC = 2 units.
In semicircle ABC, area of the shaded portion is the difference between the area of half the semicircle PBC and the area of the triangle PBC.
Triangle PBC is a right triangle because PB is perpendicular to PC. PB and PC are radii to the circle and are equal. So, triangle PBC is an isosceles triangle.
Therefore, triangle PBC is a right isosceles triangle.
Area of half the semicircle - Area of region PBC
Area of the semicircle ABC = ½ area of the circle of radius 2.
So, area of half the semicircle, PBC = ¼ area of the circle of radius 2.
Area of half the semicircle, PBC = ¼ * π * 22
Area of half the semicircle, PBC = π sq units
Area of right isosceles triangle PBC
Area of right triangle PBC = ½ PC * PB
Area of triangle PBC = ½ * 2 * 2 = 2 sq units
Area of shaded region
Area of shaded region in one of the semi circles ABC = (π - 2) sq units
Therefore, area of the overall shaded region = 2(π - 2) sq units
Choice C
Answer: C
Question: Ayayai electronics is a company manufacturing MP3 players. Ayayai manufactures only two players: iMe and iMine. Either player is assembled using a LCD screen or an OLED screen. Excluding the expensive OLED-iMine model, Ayayai manufactures 21,000 players per month. Every month, Ayayai manufactures 11,000 players with an OLED screen, and 12,000 iMine models. If Ayayai manufactures 8000 LCD iMe models monthly, how many players (of all models) does Ayayai manufacture per month?
Options:
A)24,000
B)25,000
C)26,000
D)27,000
E)28,000
Rationale: Let x be the iMine LCD players
Let y be the iMe OLED players
8000 + x + y = 21000
x + y = 13000
Assume 6000,7000 for x and y.
6000 + iMine OLED = 11000. iMine OLED = 5000.
Hence total number of players = 8000 + x + y + 5000 = 26000
ans :(Option C)
Answer: C
Question: A grocer has a sale of Rs. 5420, Rs. 5660, Rs. 6200, Rs. 6350 and Rs. 6500 for 5 consecutive months. Find the sale he should have in the sixth month, so that he gets an average sale of Rs. 6300?
Options:
A)Rs. 5870
B)Rs. 5991
C)Rs. 6020
D)Rs. 7670
E)None of these
Rationale: Explanation:
Total sale for 5 months = Rs. (5420 + 5660 + 6200 + 6350 + 6500) = Rs. 30,130
Therefore, required sale = Rs. [(6300 * 6) – 30,130] = Rs. (37800 – 30,130) = Rs. 7670
ANSWER D
Answer: D
Question: A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
Options:
A)109%
B)600%
C)100%
D)170%
E)102%
Rationale: MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer: C
Answer: C
Question: Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 25% profit?
Options:
A)15.75
B)16.33
C)16.35
D)16.3
E)16.32
Rationale: C.P. of 50 kg wheat = (30 * 11.50 + 20 * 14.25) = Rs. 630.
S.P. of 50 kg wheat = 125% of Rs. 630 = 125/100 * 630 = Rs. 787.5
S.P. per kg = 787.5/50 =15.75.
Answer: A
Answer: A
Question: The H.C.F and L.C.M of two numbers are 11 and 385 respectively. If one number lies between 75 and 125 , then that number is
Options:
A)77
B)88
C)99
D)110
E)120
Rationale: Explanation:
Product of numbers = 11 x 385 = 4235
Let the numbers be 11a and 11b . Then , 11a x 11b = 4235 inline fn_jvn Rightarrow ab = 35
Now, co-primes with product 35 are (1,35) and (5,7)
So, the numbers are ( 11 x 1, 11 x 35) and (11 x 5, 11 x 7)
Since one number lies 75 and 125, the suitable pair is (55,77)
Hence , required number = 77. Answer: A
Answer: A
Question: Taylor is making a bracelet. He Starts with 2 blue knots, 6 red knots, and 2 yellow knots, in that order, and repeats the pattern until there is no more string. If the last Knot is yellow which of the following could be the total number of knots on the bracelet.
Options:
A)89
B)79
C)95
D)97
E)102
Rationale: Repeating sequence = 2 + 6 + 2 = 10.
As the pattern ends in Y this could be the 9th thread or 10 thread (both are yellow)
Out of the answer choices, correct on should be a multiple of 10(since 10 threads are repeating) and if not, multiple of 10 + 9 (since 10 threads are repeating and last sequence end at first yellow)
none of the options is a direct multiple of 10 and only option that is multiple of 10; + 9 is 79 (10*7) + 9
Hence, answer is B
Answer: B
Question: How much to pay for a pair of jeans of $89 when discounted by 60 percent?
Options:
A)$45.5
B)$30
C)$35.6
D)$40
E)$36
Rationale: Solution
Cost of pair of jeans = $89
60 % Discount on $89 = $89*60/100 =$53.4
So cost of jean (-) Discounted price = $89-$53.4 =$35.6
Answer C
Answer: C
Question: How many litres of pure acid are there in 5 litres of a 30% solution
Options:
A)1.5
B)1.6
C)1.7
D)1.8
E)1.9
Rationale: Explanation:Question of this type looks a bit typical, but it is too simple, as below... It will be 5 * 30/100 = 1.5 Answer: Option A
Answer: A
Question: Certain stocks in January were 20% less than they were in February and 30% greater than they were in March. What was the percentage decrease in the stocks from February to March?
Options:
A)5.7%
B)11%
C)20%
D)25.3%
E)38.5%
Rationale: Let stocks value in Feb = 100 => In Jan = 80 and March = 80 * 100/130 = 61.5
Thus, percent decrease in stocks from Feb to March = 100 - 61.5 = 38.5%
Hence Answer is E
Answer: E
Question: Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
Options:
A)16
B)12
C)18
D)17
E)13
Rationale: 1/8 + 1/24 = 1/6
6 * 2 '
= 12
Answer: B
Answer: B
Question: A man can row with a speed of 14 kmph in still water. If the stream flows at 10 kmph, then the speed in downstream is?
Options:
A)28
B)26
C)20
D)87
E)24
Rationale: M = 14
S = 10
DS = 14 + 10
=24
Answer: E
Answer: E
Question: If a certain sample of data has a mean of 27.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?
Options:
A)(24.0; 28.5)
B)(24.5; 31.0)
C)(25.0; 29.5)
D)(19.5; 33.0)
E)(24.0; 29.5)
Rationale: The standard deviation is 2, so 2.5 standard deviations would be (2.5)(2) = 5.
The values between 22 and 32 are within 2.5 standard deviations from the mean.
The answer is D.
Answer: D
Question: Ajit has a certain average for 9 innings. In the tenth innings, he scores 100 runs thereby increasing his average by 8 runs. His new average is:
Options:
A)20
B)21
C)28
D)32
E)None
Rationale: Solution: Let Ajit's average be x for 9 innings. So, Ajit scored 9x run in 9 innings.
In the 10th inning, he scored 100 runs then average became (x+8). And he scored (x+8)*10 runs in 10 innings.
Now,
=>9x+100 = 10*(x+8)
Or, 9x+100 = 10x+80
Or, x = 100-80
Or, x = 20
New average = (x+8) = 28 runs
Answer: Option C
Answer: C
Question: A manufacturer is using glass as the surface for the multi-touch screen of its smartphone. The glass on the manufactured phone has a 3% probability of not passing quality control tests. The quality control manager bundles the smartphone in groups of 10. If that bundle has any smartphone that does not pass the quality control test, the entire bundle of 10 is rejected.
What is the probability that a smartphone bundle that will be rejected by quality control?
Options:
A) 0.25
B) .05^10
C) 1-0.95^10
D) 1-0.97^10
E) 0.95^10
Rationale: Find the probability of the opposite event and subtract from 1.
The opposite event is that bundle will NOT be rejected by quality control, which will happen if all 10 phones pass the test, so P(all 10 phones pass test)=0.97^10.
P(at least one phone do not pass the test)=1- P(all 10 phones pass test)=1-0.97^10.
Answer: D.
Answer: D