divelab/Sys2Bench huggingface dataset:
Question: If q persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?
Options:
A)z
B)x
C)x/y
D)z/x
E)y/z
Rationale: the Q doesn't seem to be having the any correct answer as a choice..
since we are looking for days, lets keep days in end and work out a solution..
q person can do z jobs in y days..
so q person can do 1 job in y/z days..
and 1 person can do 1 job in y^2/z days..
so y person can complete 1 job in y^2/zy=y/z..
so the answer should be y/z=E
Answer: E
Question: If 85 percent of the test takers taking an old paper and pencil GMAT exam answered the first question on a given math section correctly, and 70 percent of the test takers answered the second question correctly, and 5 percent of the test takers answered neither question correctly, what percent answered both correctly?
Options:
A)60 %
B)65 %
C)70%
D)75%
E)80%
Rationale: {Total} = {First correctly} + {Second correctly} - {Both correctly} + {Neither correctly}
100 = 85 + 70 - {Both correctly} + 5
{Both correctly} = 60.
Answer: A.
Answer: A
Question: In a certain alphabet, 16 letters contain a dot and a straight line. 30 letters contain a straight line but do not contain a dot. If that alphabet has 50 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line?
Options:
A)4
B)8
C)12
D)16
E)20
Rationale: We are told that all of the letters contain either a dot or a straight line or both, which implies that there are no letters without a dot and a line (no line/no dot box = 0).
First we find the total # of letters with lines: 16 +30 = 46;
Next, we find the total # of letters without line: 50 - 46 = 4;
Finally, we find the # of letters that contain a dot but do not contain a straight line: 4 - 0 = 4.
Answer: A
Answer: A
Question: One computer can upload 100 megabytes worth of data in 2 seconds. Two computers, including this one, working together, can upload 1300 megabytes worth of data in 10 seconds. How long would it take for the second computer, working on its own, to upload 100 megabytes of data?
Options:
A) 6.6
B) 7
C) 9
D) 11
E) 13
Rationale: Since the first computer can upload 100 megabytes worth of data in 2 seconds then in 2*10=20 seconds it can upload 10*100=1000 megabytes worth of data, hence the second computer in 20 seconds uploads 1300-1000=300 megabytes worth of data. The second computer can upload 100 megabytes of data in 6.6 seconds.
Answer: A.
Answer: A
Question: A six-sided die is rolled once. What is the probability that the number rolled is greater than 3?
Options:
A)2 / 3
B)1 / 2
C)3 / 3
D)4 / 5
E)2 / 4
Rationale: Only 4, 5 & 6 so, 3 / 6 = 1/2
correct answer B
Answer: B
Question: When positive integer m is multiplied by positive integer n, the units digit of the product is 3. Which of the following are factors of q?
I. 8
II. 15
III. 30
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)None of the above
Rationale: ans E..
we can tell the ans w/o using examples..
the units digit of product m*q is 3..
this means m and q are odd positive integers..
therefore q cannot have an even factor so 8 and 30 are out..
q cannot have a factor ending in 5 because in that case the units digit has to be 5 or 0... so 15 is also out
Answer: E
Question: Before 2 years, dog A’s age was 4 times of dog B’s age and after 4 years, dog A’s age will be 3 times of dog B’s age. What is the difference of dog A’s age and dog B’s now?
Options:
A)36
B)42
C)54
D)60
E)64
Rationale: A - 2 = 4(B - 2) --> A - 4B = -6.............1
A + 4 = 3(B + 4) --> A - 3B = 8.............2
(2) - (1) --> B = 14 --> A = 3(18) = 50
A - B = 50 - 14 = 36
Answer: A
Answer: A
Question: An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
Options:
A)180degree
B)160degree
C)120degree
D)150degree
E)170degree
Rationale: We know that angle traced by hour hand in 12 hrs = 360°
From 8 to 2, there are 6 hours.
Angle traced by the hour hand in 6 hours = 6×360/12=180°
Answers is A.
Answer: A
Question: Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, Annie is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week Annie worked a total of 44 hours. If Harry and Annie were paid the same amount last week, how many hours did Harry work last week?
Options:
A)40
B)42
C)44
D)46
E)48
Rationale: Annie earned 40x + 4(2x) = 48x
Let H be the number of hours that Harry worked.
Harry earned 30x + 1.5x(H-30) = 48x
(1.5x)(H) = 63x
H = 42 hours
The answer is B.
Answer: B
Question: In a certain store, the profit is 100% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
Options:
A)30%
B)70%
C)37.5%
D)250%
E)120%
Rationale: Let C.P. = Rs. 100. Then, profit = Rs. 100, S.P. = Rs. 200
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 200
Profit = 200 - 125 = Rs. 75
Required percentage = 75/200 * 100 = 37.5%
ANSWER:C
Answer: C
Question: Mrs. Angel. invested $24,000; part at 5%, and part at 8%. The total interest on the investment was $1,680. How much did she invest at each rate?
Options:
A)x=$13,000, y =$26,000
B)x=$8,000, y =$16,000
C)x=$14,000, y =$28,000
D)x=$15,000, y =$30,000
E)x=$18,000, y =$36,000
Rationale: I approached this question like a mixture problem.
I don't like the wordingpartat 5% andpartat 8% because we have variables x and y in the answer choices and I have no idea which one is x or y.
Anyway here's how I did it.
0.05(x) + 0.08(y) = 0.07(x+y)
0.01(y) = 0.02(x)
y = 2x
Note: 0.07(x+y) because $1,680 is 7% of 24,000
In which answer choice is y = 2(x)
Answer B
Answer: B
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.500, what is the reduced price for kg?
Options:
A)25
B)60
C)70
D)80
E)20
Rationale: A
500*(25/100) = 125 ---- 5
? ---- 1 => Rs.25
Answer: A
Question: The Simple interest and the true discount and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum is :
Options:
A)Rs. 1800
B)Rs. 1450
C)Rs. 1360
D)Rs. 6800
E)None
Rationale: Solution
Sum =S.I xT.D./ ( S.I ) - ( T.D. ) = 85x80/85 - 80 = Rs. 1360.
Answer C
Answer: C
Question: A committee of three people is to be chosen from 5 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
Options:
A)16
B)24
C)26
D)30
E)80
Rationale: Total no of ways of choosing a committee = 10C3 = 120
No of ways to choose first couple = 5C1 = 5
No of ways to choose 1 person from remaining 8 = 8C1 = 8
Total number of ways of choosing a married couple to be in the same committee = 5*8=40
So, no of ways not choosing a married couple = 120-40 =80
ANS:E. 80
Answer: E
Question: A set of 14 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?
Options:
A)32
B)37
C)42
D)43
E)50
Rationale: The correct answer is D.
A set of 14 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?
Given 14 different integers, lets say
n1, n2, n3, n4, n5, n6, n7, n8, n9, n10, n11, n12, n13, n14, n15
Also given median is 25 i.e. n8 = 24
n1, n2, n3, n4, n5, n6, n7, 25, n9, n10, n11, n12, n13, n14, n15
As each integer is different we need to find the maximum values for all those numbers before the median.
the maximum value n7 can have is one less then the median i.e. 24, similarly n6 will be one less than 24 i.e. 23 ... using this process the values for all number before the median would be..
18, 19, 20, 21, 22, 23, 24, 25, n9, n10, n11, n12, n13, n14, n15
Also given the range is 25 i.e. n15 - n1 (18) = 24
The maximum value n15 can have is 24 + n1 (18) = 42
C
Answer: C
Question: Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is?
Options:
A)81.6
B)81.9
C)81.2
D)81.3
E)81.1
Rationale: SI = 40 + 40
CI = 40 + 40 + 1.6 = 81.6
Answer: A
Answer: A
Question: The amount of electrical current that flows through a wire is inversely proportional to the resistance in that wire. A wire originally carries 4 amperes of electrical current. Then the resistance is reduced to one-half of its original value. How many amperes of electrical current will flow through the wire?
Options:
A)1
B)2
C)4
D)8
E)12
Rationale: Given that, I∝1/R, I*R is a constant value.
I1*R1 = I2*R2
I1*R1 = I2*R1/2
I2 = 2*I1 = 8 amperes
The answer is D.
Answer: D
Question: A photo-mat shop charges $0.55 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $33 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 = 0.55
Subsequent = 0.55*0.6=0.33
Price of 1 full film=0.55+0.33*35=12.1
Price of 4 full film = 12.1*2=24.2
33-24.2=8.8
8.8=0.55+0.33x
x=25
33--->2 full films and 1+25=26 photos
Answer: A
Answer: A
Question: What is the sum of all three digit integers formed using the digits 2,3 and 4 (repetition is allowed)
Options:
A)4444
B)6100
C)8991
D)7110
E)8800
Rationale: n = 3*3*3 = 27
= (444 + 222) / 2 = 333
Sum = number of integers x average value
n * = 27 * 333 = 8991
answer = C
Answer: C
Question: If a tap could fill entire tank in 15 hrs due to leakage, then in how much time
tank can be emptied by leakage if tap can fill entire tank in 12 hrs without leakage
Options:
A)12hrs
B)24hrs
C)60hrs
D)48hrs
E)52hrs
Rationale: time take to fill[withleakage] =15hrs so workdone in 1hr=1/15
time tkae to fill[without leakage]=12hrs so workdone in 1hr=1/12
if u subtract both u'll get time taken by leakage to empty...
1/15-1/12=1/60 so 60hrs
ANSWER:C
Answer: C
Question: A train traveling at 72 kmph crosses a platform in 35 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?
Options:
A)340 meters
B)360 meters
C)420 meters
D)600 meters
E)Cannot be determined
Rationale: Speed of train = 72 * (5/18) = 20 m/s
Lets consider the man as a stationery point on the platform.
Crossing the point gives us the length of the train.
Lt = 20 * 18 = 360 m.
Crossing the platform gives us the length of trainlength of platform.
L(t+p) = 20 * 35 = 700 m.
So, length of platform = 700 - 360 = 340 m
IMO, Answer
A
Answer: A
Question: Baby Isabel plays with blocks. Each block is 3.7 inches tall. She has a collection of 41 blocks. If she could stack all of the blocks up one on top of the other, how many inches tall would her tower of blocks be?
Options:
A)67"
B)90"
C)106"
D)120"
E)151.7"
Rationale: 3.7"*41=151.7". Answer is E.
Answer: E
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)299 m
B)188 m
C)500 m
D)188 m
E)182 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: A train is moving at a speed of 90km/hr and its length is 500m. Find the time taken by it to pass a man standing near the railway line?
Options:
A)30sec
B)45sec
C)36sec
D)20sec
E)52sec
Rationale: Speed of the train = 90*5/18 = 25 m/sec
Distance moved in passing the standing man = 500m
Required time taken = 500/(25) = 20sec
Answer is D
Answer: D
Question: A set of 11 positive integers has an average of 15. Which of the following is the greatest possible value for the median of this set?
Options:
A)26
B)30
C)36
D)45
E)46
Rationale: for the median to be max , we should take all the values below meadian to be the lowest and the remaining values to be the same..
here 1 is the lowest value(positive int) so the lowest 5 int will equal 5..
remaining 6= 15*11-5=160..
therefore each valueof these 6 int =160/6=26
ans A
Answer: A
Question: How many integers between 100 and 500 are there such that their unit digit is even?
Options:
A)100
B)120
C)200
D)50
E)150
Rationale: 400 numbers between - 100 and 400
Out of which half would be even, half odd.
Number of even unit digit number = 200.
correct option is C
Answer: C
Question: Which of the following fractions is not a terminating decimal?
Options:
A)2/3
B)3/4
C)4/5
D)7/8
E)9/10
Rationale: 2/3 = recurring fraction of 0.6666
3/4 = 0.75
4/5 = 0.80
7/8 = 0.875
9/10 = 0.90
Answer : A
Answer: A
Question: In a queue if 30 children were made to stand in a column, 16 columns could be formed. If 24 children were made to stand in a column, how many columns could be formed?
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: Sol. Required number = 16 *^30 = 20
B
Answer: B
Question: How many different arrangements of A, B, C, D, E AND F are possible where A is not adjacent to B and D is not adjacent to E?
Options:
A)96
B)48
C)32
D)144
E)1
Rationale: So you have A,B,C,D,E,F
five possible ways to arrange it = 6! = 720
AB cannot be adjacents neither DE:
(AB),C,D,E,F = 5! =120 x 2(because it can be (AB) or (BA) ) = 240
A,B,C,(DE) = 5! = 120 x 2 = 240
To get rid of the double counting:
(AB),C,(DE),F = 4! x 4 = 96
(Four possible ways to arrange it)
720 -240-240+96 = 144 possible ways
D
Answer: D
Question: A class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the class room ?
Options:
A)115
B)117
C)116
D)114
E)112
Rationale: Explanation:
Length = 6 m 24 cm = 624 cm
Width = 4 m 32 cm = 432 cm
HCF of 624 and 432 = 48
Number of square tiles required = (624 x 432)/(48 x 48) = 13 x 9 = 117.
Answer IS B
Answer: B
Question: Due to construction, the speed limit along an 12-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options:
A) 4
B) 5
C) 6
D) 7
E) 8
Rationale: 12/35 - 12/55 = 12/5 * ( 11 - 7)/77
= 12/5 * 4/77 * 60 min
= 12 * 12 * 4/77
= 576/77 ~ 7.4
Answer - D
Answer: D
Question: John works full-time, 40 hours a week, selling cars at the local auto mall. His sales quota for a week is $20,000. How much does John have to sell per hour to make his sales quota?
Options:
A)200
B)250
C)500
D)1000
E)700
Rationale: There are 40 hours in a work week. If his quota is $20,000, then we simply divide 40 by $20,000.
20,000 / 40 = 500.
Therefore, John has to sell at least $500 per hour to meet his weekly quota of $20,000.
Thus, the correct answer is C.
Answer: C
Question: Walking 7/8th of its usual speed a man is 6 minutes too late the usual time taken by him to cover that distance is?
Options:
A)15min
B)1hr 5 min
C)1hr 8 min
D)42min
E)52min
Rationale: need speed =7/8 of the used speed
new time= 8/7 of usual time
(8/7 of the usual time)- (usual time)=1/10hr
1/ 7 of the usual time=1/10
usual time =7/10=42 min
Answer(D)
Answer: D
Question: how many 6 digits numbers have all their digits either all odd or all even?
Options:
A)27125
B)28125
C)29125
D)26125
E)25125
Rationale: With all even digits=4*5^5 (Even digits->0,2,4,6,8)
2 _ _ _ _ _ | 4 _ _ _ _ _ | 6 _ _ _ _ _ | 8 _ _ _ _ _ (the gaps can be filled by any of the no.s 0,2,4,6,8)
with all odd digitd=5*5^5
1 _ _ _ _ _| 3 _ _ _ _ _| 5 _ _ _ _ _| 7 _ _ _ _ _ |9 _ _ _ _ _ (The gaps can be filled with any of 1,3,5,7,9)
So, total number of 6digit no. with all digits odd or all even is:
(4*5^5)+(5*5^5)=12500+15625=28125
ANSWER:B
Answer: B
Question: A, B and C entered into a partnership. A invested Rs. 2,560/- and B invested Rs. 1105/-, out of which A got Rs 320. C’s capital was
Options:
A)Rs. 2840/-
B)Rs. 4028/-
C)Rs. 4280/-
D)Rs.4820/-
E)None of these
Rationale: Explanation:
Let A : B : C = 2560 : 2000 : x. Then,
A’s share = [1105 * 2560/(4560 + x)]
Therefore (1105 * 2560)/(4560+x) = 320 => 4560 + x = (1105 * 2560)/320 = 8840
= x = 8840 – 4560 = Rs. 4280/-
Hence, C’s capiatal Rs 4280/-
Answer: Option C
Answer: C
Question: Five times the fifth term of an A.P is equal to six times the sixth term of the A.P, What is the value of the eleventh term?
Options:
A)1
B)5
C)0
D)2
E)3
Rationale: 5( a + 4d ) = 6 ( a + 5d ), 5a + 20d = 6a + 30d, a + 10d = 0,
i.e 11 th = 0
ANSWER:C
Answer: C
Question: How many 1/8s are there in 37 1/2?
Options:
A)300
B)400
C)500
D)600
E)700
Rationale: Required number = (75/2)/(1/8)
= (75/2 x 8/1)
= 300.
ANSWER:A
Answer: A
Question: During the first two weeks of January, the total rainfall in Springdale was 25 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall during the second week of January?
Options:
A)5 inches
B)6 inches
C)9 inches
D)10 inches
E)15 inches
Rationale: Total rainfall in 2 weeks = 25 inches.
Assume the rainfall in second week = 1.x
Rainfall in first week = x
Total rainfall = 2.5x =25 inches
x = 10 and 1.5x = 15
Rainfall during second week = 9 inches
Option E
Answer: E
Question: The equation x = 2y^2 + 5y - 18, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is
Options:
A)3x + y - 20 = 0
B)y - 3x - 11 = 0
C)-3x + y - 15 = 0
D)-2x - y - 7 = 0
E)-3x + y + 13.5 = 0
Rationale: The question is made to look difficult though it is pretty simple if you focus on just the line and use process of elimination. (Remember that GMAT does not focus on parabolas so basically, the question should be quite do-able even if someone doesn't know how to handle parabolas.)
The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant).
In options B ,C D and E, if you put x = -5, you get -ve value for y co-ordinate. So ignore them.
Answer must be (A)
Answer: A
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 100 years now, the son's age five years back was:
Options:
A)45 years.
B)40 years.
C)30 years.
D)35 years.
E)50 years.
Rationale: Let the son's present age be x years. Then, (100 - x) = x
2x = 100.
x = 50.
Son's age 5 years back (50 - 5) = 45 years.
Answer: Option A
Answer: A
Question: There are 8 magazines lying on a table; 4 are fashion magazines and the other 4 are sports magazines. If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?
Options:
A)1/2
B)2/3
C)32/35
D)11/12
E)13/14
Rationale: Total probability=8C3=56
4C3 +4C2*4C1+4C1*4C2=4+24+24=52
therefore the probability that at least one of the fashion magazines will be selected= 52/56=13/14
answer is E
Answer: E
Question: find the number of 6 digit numbers that can be formed using digits 1,2,3,4,5,6 once such that the 6digit number is divisible by its unit digit.
Options:
A)646
B)648
C)650
D)652
E)654
Rationale: There are 6 numbers which can be placed in units digits.
case 1: When the unit digit is 1,2,3,5,6 whatever the other numbers are the 6 digit number will be surely divisible by the unit digit.
Hence the 5 numbers in the units place can be placed in 5 ways and the remaining 5 numbers can be arranged in 5! ways.
5*5!=600 ways
Case 2: If the unit digit is 4, then the tens digit should be 2 or 6, hence 24 or 64 can be arranged in the last two places in 2 ways and the remaining 4 numbers can be arranged in 4 places in 4!ways.
2*4!=48 ways
Total no.of.ways= 600+48 = 648 ways.
ANSWER:B
Answer: B
Question: Health insurance Plan E requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?
Options:
A)$600
B)$1000
C)$3800
D)$5300
E)$6200
Rationale: 0.5 * 600 = 300 where E = B.
Answer: B
Question: A man buys Rs. 60 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:
Options:
A)s. 12
B)s. 15
C)s. 18
D)s. 21
E)s. 45
Rationale: Dividend on Rs. 60 = Rs.	9/100	x 60 =Rs.	5.4	.
Rs. 12 is an income on Rs. 100.
Rs.	5.4	is an income on Rs.100/12 x 5.4	= Rs. 45.
Answer: Option E
Answer: E
Question: In the formula V = 1/(2r)^4, if r is halved, then V is multiplied by
Options:
A)8
B)64
C)1
D)1/8
E)2
Rationale: Say r=2 => V1 = 1/32
when r=1; V2 = 1/16
V2 = 2*V1.
Answer=E=2
Answer: E
Question: Select the non termination decimal among the following.
Options:
A)5/3
B)3/4
C)4/5
D)7/8
E)9/10
Rationale: A. Non terminating decimal means that 5/3 = 1.66666 and so on.
Answer: A
Question: 36, 34, 30, 28, 24, 22, 18, ?
Options:
A)16
B)14
C)12
D)10
E)8
Rationale: This is an alternating number subtraction series. The pattern is -2, -4, -2, ....
The answer is A.
Answer: A
Question: The ratio of the areas of two squares, one having double its diagonal then the other is:
Options:
A)2:1
B)1:2
C)2:3
D)1:4
E)4:1
Rationale: Lenth of the diagonals be 2x and x units.
areas are 1/2 × (2x)power2 and (1/2 × (xpower2))
Required ratio = 1/2 × 4 x2 : 1/2 x2 = 4 : 1
Answer is E.
Answer: E
Question: Annika hikes at a constant rate of 10 minutes per kilometer. She has hiked 2.5 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 45 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 45 minutes, for how many kilometers total did she hike east?
Options:
A)3.625
B)3.5
C)4
D)4.5
E)5
Rationale: Set up two R x T =D cases.
1. 1/10 km/ min x T = 2.5
from which T= 25 mins.
We know total journey time now is 45 +25 = 70
The rate is the same ie 1/10km/min.
set up second R x T =D case.
1/10 km/min x 70 = 7 km
Now the total journey would be halved as distance would be same in each direction. 7/2 =3.5
B.
Answer: B
Question: What is the probability that a number selected from numbers 1,2,3,...,30, is prime number, when each of the given numbers is equally likely to be selected?
Options:
A)1011
B)1041
C)9018
D)1030
E)1020
Rationale: X={2,3,5,7,11,13,17,19,23,29}X={2,3,5,7,11,13,17,19,23,29}
n(X)=10,n(S)=30
Hence required probability,
=n(X)n(S)
=1030
D
Answer: D
Question: Find the unit's digit in 264^102 + 264^103
Options:
A)zero 0
B)1
C)2
D)4
E)5
Rationale: Required unit's digit = unit's digit in 4102+4103.4102+4103.
Now, 4242 gives unit digit 6.
⇒ 41024102 gives unit digit 6.
⇒ 41034103 gives unit digit of the product 6×46×4 i.e., 4.
Hence, unit's digit in 264102 +264103264102+264103
= unit's digit in (6+4)=0
A
Answer: A
Question: For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 181 books with me to gift her.
Can you calculate, on which day is our anniversary?
Options:
A)31
B)18
C)23
D)33
E)25
Rationale: B
18rd day
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 = 181
Thus our anniversary falls on the 18rd day of the month.
You can apply other formulas to shorten the process but that is the simplest way to do it.
Answer: B
Question: An agent, gets a commission of 2.5% on the sales of cloth. If on a certain day, he gets Rs. 15 as commission, the cloth sold through him on that day is worth
Options:
A)333
B)600
C)887
D)299
E)132
Rationale: Explanation:
Let the total sale be Rs. x.
Then, 2.5%. of x = 15 <=> (25/10 * 1/100 * x) = 15 <=> x = 600.
Answer: B)
Answer: B