divelab/Sys2Bench huggingface dataset:
Question: In how many ways can 5 identical black balls and 7 identical white balls be arranged in a row so that no 2 black balls are together
Options:
A)56
B)64
C)65
D)316
E)560
Rationale: Consider the possible arrangements:
WBWBWBWBWBWW or BWBWBWBWBWWW or WWBWBWBWBWBW or WWWBWBWBWBWB
Clearly, we are concerned about not placing 2 B's together, whites can be placed however we want.
So, it is like _W_W_W_W_W_W_W_ where black ball can be placed anywhere on the blank spaces, and this way, there never will be a case where 2 black balls fall together.
As there are 8 black spaces where 5 black balls can be placed, thus, the combination turns out as 8C5 (again, we are not concerned about the placement of white balls as we have already "fixed" their positions in the diagram above)
Also, we achieved at 8C5 as arranging 5 black balls on 8 different spots => 8!/5!3! (Total combination of available spaces = 8!; choosing 5 spaces out of them = 5!, arranging 3 leftover spaces = 3!) = 56
Hence answer is A
Answer: A
Question: How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
Options:
A)360
B)88
C)77
D)121
E)123
Rationale: The given digits are six.
The number of four digit numbers that can be formed using six digits is ⁶P₄ = 6 * 5 * 4 * 3
= 360.
Answer: A
Answer: A
Question: The length of the bridge, which a train 155 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)76 m
B)178 m
C)220 m
D)187 m
E)176 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (155 + x)/30 = 25/2
=> 2(155+ x)= 750 => x = 220 m.
Answer: C
Answer: C
Question: If v and d are both integers, v>d, and -3v>19, then the largest value of d would be?
Options:
A)-5
B)-6
C)-7
D)-8
E)-10
Rationale: No, your thinking is incorrect. When we know that v>d and v<-6.33, the largest value of v can be -7 while if v=-7, then largest value of d < -7 will be -8.For negative numbers, -7 > -8 and -8> -10.
You are right in saying that d can take any value less than -7 ---> d could be -8, -9, -10 .... and out of all these values, -8 is the greatest.
Look at the numbers on the number line. For any 2 numbers, the ones on the right are greater than the ones on the left:
.......-11 -10 -9 -8 -7 -6 -5 ..... 0 1 2 3 4 5 6 ... (-11< -10, -10< -8, 4< 5 etc).
So, as per the question if d<v and v = -7 , then d's largest 'possible' value has to be -8.
-10 is smaller than -8=D
Answer: D
Question: GOOD is coded as 164 then BAD coded as 21.if ugly coded as 260 then ADD?
Options:
A)20
B)30
C)29
D)27
E)28
Rationale: GOOD=(7+15+15+4)*4=164
BAD= (2+1+4)*3=21
UGLY= (21+7+12+25)*4=260
coding follows
(sum of position of alphabets)*(no. of letters in the given word)
so,
ADD=(1+4+4)*3= 27
ANSWER:D
Answer: D
Question: What is the smallest positive integer x, such that 1944x is a perfect cube?
Options:
A)4
B)3
C)8
D)12
E)18
Rationale: Take out the factors of 1944 that will come 2^3*3^3 *3^2. for perfect cube you need every no. raise to the power 3. for 1944 to be a perfect cube, need 1 3 that means =3
B is the answer.
Answer: B
Question: (2^2+4^2+6^2+.....+14^2)=?
Options:
A)88
B)560
C)99
D)550
E)540
Rationale: =(1x2)^2+(2x2)^2,+(2x3)^3+......(2x7)^2
=2^2 x (1^2+2^2+3^2+.......+7^2)
formula is =1/6 n(n+1)(2n+1)
=(4x1/6x7x8x15)
=(4x140)=560
Answer is B
Answer: B
Question: A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was:
Options:
A)90
B)100
C)110
D)140
E)150
Rationale: sax Letlheo g alnumberofworkers hex
x workers can do the wor - 100 days
(x — 10) workers can do the work in 110 days
4 100x 1u1x— 10)
1100 Q x 110
C
Answer: C
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
Options:
A)1
B)8
C)9
D)7
E)4
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Answer: B
Question: Three integers are at random chosen between 0 and 9 inclusive. What is the probability K that each number is different ?
Options:
A)A.18/25
B)B.4/5
C)C.81/100
D)D.9/10
E)E.1
Rationale: Number of ways of choosing the 3 integers without restriction = 10 * 10 * 10
Number of ways of choosing the 3 integers so that the 3 integers are different = 10 * 9 * 8
Probability K= 10 * 9 * 8/10 * 10 * 10 = 72/100 = 18/25
Answer: A
Answer: A
Question: A train 50m long takes 6 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train?
Options:
A)15kmph
B)25kmph
C)35kmph
D)45kmph
E)55kmph
Rationale: Let the speed of the train be x kmph
Speed of the train relative to man = x+5 = (x+5)*5/18 m/sec
50/[(x+5)*5/18] = 6
30(x+5) = 900
x = 25kmph
Answer is B
Answer: B
Question: If in a race of 90m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by:
Options:
A)20m
B)16m
C)11m
D)10m
E)18m
Rationale: Explanation:
The difference in the timing of A and B is 5 seconds. Hence, A beats B by 5 seconds.
The distance covered by B in 5 seconds = (90 * 5) / 25 = 18m
Hence, A beats B by 18m.
ANSWER E
Answer: E
Question: Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/11 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now?
Options:
A)$110
B)$120
C)$183.3
D)$220
E)$260
Rationale: Lets assume Al have amount A in his bank account and Eliot's bank account got E amount. We can form an equation from the first condition.
A-E = 1/11*(A+E) ==> 10A = 12E ------------ (1)
Second condition gives two different amounts, Al's amount = 1.1A and Eliot's amount = 1.2E
1.1A = 22 + 1.2E ==> 11A =220 +12E -------(2)
Substituting (1) in (2):
11A = 220+10A ==>A = 220 ;E =183.3
C
Answer: C
Question: Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
Options:
A)540
B)325
C)600
D)455
E)200
Rationale: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
ANSWER A
Answer: A
Question: The number of singles that a baseball player hit increased 10 percent from her first season to her second season, and the number of doubles that she hit in the same time period decreased by 1 percent. If the total number of singles and doubles that she hit increased 3 percent from her first season to her second season, what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season?
Options:
A)2:3
B)3:5
C)4:7
D)5:8
E)7:9
Rationale: Soln:-
1.10S + 0.99D = 1.03[S + d]
0.07S = 0.04D
S/D = 4/7
ANSWER:C
Answer: C
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A?
Options:
A)240
B)177
C)266
D)155
E)141
Rationale: (3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240
Answer:A
Answer: A
Question: Two taps can separately fill a cistern 10 minutes and 12 minutes respectively and when the waste pipe is open, they can together fill it in 20 minutes. The waste pipe can empty the full cistern in?
Options:
A)6.5
B)7.5
C)8.5
D)9.5
E)2
Rationale: 1/10 + 1/12 - 1/x = 1/20
x = 7.5
Answer:B
Answer: B
Question: The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 10 years, son's age will be:
Options:
A)12 years
B)14 years
C)18 years
D)24 years
E)26 years
Rationale: Explanation:
Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
54 - x = 5x - 30
6x = 84
x = 14.
Son's age after 10 years = (x+ 10) = 24 years..
Answer: D
Answer: D
Question: Anthony and Cindy were each given X dollars in advance for each day they were expected to perform at a community festival. Anthony eventually performed on all 14 days of the festival, while Cindy performed on 4 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance, in terms of Y?
Options:
A)2Y
B)4Y
C)5Y
D)6Y
E)10Y
Rationale: Money Anthony got = 14X for performance + y from Cindy
So Anthony's daily allowance = (14X+y)/14
Cindy's daily allowance = (14x-y)/10
These 2 quantities are same - so (14X+y)/14 = (14X-y)/10
so 140X +10y = 196X - 14y or y=(7/3)x.
So money Anthony got in advance = 14X = 6Y.
Answer = D.
Answer: D
Question: Stacy has a 63 page history paper due in 7 days. How many pages per day would she have to write to finish on time?
Options:
A)9
B)8
C)10
D)8.5
E)6
Rationale: 63/7=9
A.9
Answer: A
Question: A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 12 hours longer than the first half, how many hours did it take the runner to run the second half?
Options:
A)20
B)22
C)24
D)26
E)28
Rationale: The runner runs the first 20 miles at speed v and the second 20 miles at speed v/2.
The time T2 to run the second half must be twice the time T1 to run the first half.
T2 = 2*T1 = T1+12
T1 = 12 and so T2 = 24.
The answer is C.
Answer: C
Question: Andrew purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
Options:
A)1000
B)1055
C)1060
D)1075
E)1080
Rationale: Cost of 8 kg grapes = 70 × 8 = 560.
Cost of 9 kg of mangoes = 55 × 9 = 490.
Total cost he has to pay = 560 + 490 = 1055
B
Answer: B
Question: X and Y started a business by investing Rs.36000 and Rs.42000 respectively after 4 months Z joined in the business with an investment of Rs.48000, then find share of Z in the profit of Rs.13860 ?
Options:
A)4032
B)4000
C)3250
D)3825
E)3985
Rationale: Ratio of investment, as investments is for different time.
Investment x Number of units of time.
Ratio of investments X : Y : Z = 36000 : 42000 : 48000 => 6 : 7 : 8.
X = 6 x 12 Months = 72, Y = 7 x 12 = 84, Z = 8 X 8 = 64 => 18 : 21 : 16.
Ratio of investments => X : Y : Z = 18 : 21 : 16.
Investment Ratio = Profit sharing Ratio.
Z = 13860 Ã— 16/55 = Rs.4032.
Share of Z in the profit is Rs.4032.
Option A
Answer: A
Question: A man can row his boat with the stream at 14 km/h and against the stream in 4 km/h. The man's rate is?
Options:
A)1 kmph
B)4 kmph
C)5 kmph
D)7 kmph
E)8 kmph
Rationale: DS = 14
US = 4
S = ?
S = (14 - 4)/2 = 5 kmph
Answer: C
Answer: C
Question: If 5 Men or 8 Women take 5 days to complete some work, how many days will 12 Men and 8 Women working together take to complete the work?
Can anyone explain please?
Options:
A)1. 3/2 days
B)2. 2 Days
C)3. 9/4 days
D)4.25/17 days
E)5.3 days
Rationale: 5 men or 8 women takes 5 days to complete the work
So 5M = 8W
W = 5/8M
1 man in 1 day does 1 unit of work
so 5 M in 5 M = 25 units of work
now 12 M and 8 W = 12 M + 8(5/8)M
= 12M + 5M
= 17M
Since both set do the same work
17M in n Days = 25 units of work
n = 25/17 days.
D
Answer: D
Question: Rob also compared the Empire State Building and the Petronas
Towers. What is the height difference between the two if the Empire
State Building is 480m tall and the Petronas Towers is 516m tall?
Options:
A)9
B)17
C)23
D)36
E)12
Rationale: 516-480=36.Answer is D.
Answer: D
Question: Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 216 marks in the second test and failed by 36 marks in that test. Find the pass mark in the first test?
Options:
A)768
B)243
C)246
D)625
E)224
Rationale: Let the maximum mark in each test be M.
The candidate failed by 36 marks in the second test.
pass mark in the second test = 216 + 36 = 252
45/100 M = 252
Pass mark in the first test = 40/100 M = 40/45 * 252 = 224.
Answer:E
Answer: E
Question: What is x if x + 3y = 10 and y = 3?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Substitute y by 3 in x + 3y = 10
x + 3(3) = 10
x + 9 = 10
If we substitute x by 1 in x + 9 = 10, we have 1 + 9 = 10. Hence
x = 1 correct answer A
Answer: A
Question: Evaluate combination
98C96=98!/(96)!(2)!
Options:
A)1617
B)4753
C)1417
D)4353
E)None of these
Rationale: Explanation:
nCr=n!/(r)!(n−r)!
98C96=98!/(96)!(2)!
=98∗97*96!/(96)!(2)!
=98*97/2∗1
=4753
Option B
Answer: B
Question: The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
Options:
A)4
B)5
C)8
D)7
E)8
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35
So 30x + 35 + 31(x + 1) = > x = 4.
ANSWER A
Answer: A
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
Options:
A)377
B)367
C)237
D)245
E)267
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer: D
Answer: D
Question: If a 3-number code is formed of the integers from 1 to 16 inclusively, and each of the numbers in the code is different, how many possible codes are there?
Options:
A)3140
B)3250
C)3360
D)3470
E)3580
Rationale: 16*15*14=3360
The answer is C.
Answer: C
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
Options:
A)4
B)6
C)8
D)5
E)1
Rationale: Let rate = R% and time = R years.
Then, (1200 * R * R) / 100 = 432
12R2 = 432
R2 = 36 => R = 6.
Answer: B
Answer: B
Question: How many integers are there between 55 and 95, inclusive?
Options:
A)41
B)55
C)56
D)57
E)58
Rationale: I guess the easiest way to answer this is -
Say you have two positive integers, x and y where y > x
Then the number of integers between x and y is given by - (y - x) + 1
In this case, it's (95 - 55) + 1 = 41. Option A
Answer: A
Question: In how many different ways can the letters of the word 'JUDGE' be arranged such that the vowels always come together?
Options:
A)None of these
B)48
C)32
D)64
E)57
Rationale: Explanation :
The word 'JUDGE' has 5 letters. It has 2 vowels (UE) in it and these 2 vowels should
always come together. Hence these 2 vowels can be grouped and considered as a single
letter. That is, JDG(UE).
Hence we can assume total letters as 4 and all these letters are different.
Number of ways to arrange these letters = 4!= 4 x 3 x 2 x 1 = 24
In the 2 vowels (UE), all the vowels are different.
Number of ways to arrange these vowels among themselves = 2! = 2 x 1 = 2
Total number of ways = 24 x 2 = 48. Answer : Option B
Answer: B
Question: Four different children have jelly beans: Aaron has 3, Bianca has 7, Callie has 8, and Dante has 11. How many jelly beans must Dante give to Aaron to ensure that no child has more than 1 fewer jelly beans than any other child?
Options:
A) 2
B) 3
C) 4
D) 5
E) 6
Rationale: Since Bianca and Callie are both within 1 jelly bean of each other and Aaron has 5, Dante must provide 3 of his 11 jelly beans so each child has no more than 1 fewer jelly bean than any other child.
Dante + Aaron = 11+3 =14/2 = 7
11-7 = 4 so Dante must provide 3 jelly beans to Aaron.
Answer (C)
Answer: C
Question: At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
Options:
A)12
B)15
C)17
D)19
E)11
Rationale: In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.
Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.
This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.
Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.
Answer: A
Question: A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 900 grams. Find the profit percent.
Options:
A)100/17%
B)100/23%
C)100/9%
D)100/13%
E)None of these
Rationale: Explanation:
(100 + g) / (100 + x) = True measure / Faulty measure
x = 0
true measure = 1000
faulty measure = 900
100 + g / 100 + 0 = 1000 / 900
100+g = 10/9*100
g = 100/9 %
ANSWER: C
Answer: C
Question: The price of a T.V. set worth Rs. 40000 is to be paid in 20 installments of Rs. 2500 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
Options:
A)29997
B)28088
C)27098
D)37500
E)2799
Rationale: Money paid in cash = Rs. 2500
Balance payment = (40000- 2500) = Rs. 37500.
Answer:D
Answer: D
Question: Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years.
Options:
A)Rs.420.20
B)Rs.319.06
C)Rs.306.04
D)Rs.294.75
E)Rs.295.75
Rationale: A = 5000(51/50)3
= 5306.04
5000
-----------
306.04
ANSWER:C
Answer: C
Question: From an island, it is possible to reach the mainland by either Ferry P or Ferry Q. Ferry P travels for 3 hours at 8 kilometers per hour, while Ferry Q takes a route that is three times longer. If Ferry P is slower than Ferry Q by 1 kilometer per hour, how many hours longer is the journey of Ferry Q compared with the journey of Ferry P?
Options:
A)5
B)7
C)8
D)10
E)12
Rationale: The distance traveled by Ferry P is 24 km.
Then the distance traveled by Ferry Q is 72 km. Ferry Q travels at a speed of 9 kph. The time of the journey for Ferry Q is 72/9 = 8 hours, which is 5 hours more than Ferry P. The answer is A.
Answer: A
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
Options:
A)8
B)10
C)12
D)14
E)15
Rationale: 4/12 + x/15 = 1
x = 10 min
ANSWER B
Answer: B
Question: The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 6 shirts each of them then average number of shirt each of them now has
Options:
A)66
B)63
C)62
D)can't be determined
E)None of these
Rationale: Answer
Required average
= Old average + New average
= 60 + 6 = 66
Correct Option: A
Answer: A
Question: If James has to pay 12 % interest per year on an amount of $60,000 for 12 year then what is total interest paid?
Options:
A)33000
B)35410
C)36074
D)35973
E)32158
Rationale: For simple interest, I = P * N * R / 100
let Principle P = x
I = x * 12 * 12 / 100
I = 1.44 * x
Amount = P + I
60000 = 1.44 x + x
x = 24590.16 = P
I = 1.44 * 24590.16
I = 35409.83
B
Answer: B
Question: By approximately what percent is x greater than 5/11 if (4/11)(x) = 1?
Options:
A)730%
B)560%
C)410%
D)505%
E)209%
Rationale: what percent is x greater than 5/11 if (4/11)(x) = 1?
=> x = 11/4
% change =[(11/4 -5/11) /(5/11) ] * 100
= 505%
Ans ,D
Answer: D
Question: Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.16 per cubic meter?
Options:
A)2998
B)2799
C)2890
D)1485
E)1584
Rationale: 22/7 * 14 * 3/2 * 3/2
= 99 m2
99 * 16
= 1584
Answer:E
Answer: E
Question: A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many E acres were used for corn?
Options:
A) 188
B) 258
C) 376
D) 470
E) 517
Rationale: consider 5x acres of land used for bean
consider 2x acres of land used for wheat
consider 4x acres of land used for corn
Total given is 1034 acres
11x =1034
x = 94
land used for corn E= 4 * 94 = 376
correct option - C
Answer: C
Question: The cash difference between the selling prices of an book at a profit of 4% and 6% is $3. The ratio of the two selling prices is:
Options:
A)55:23
B)52:33
C)52:53
D)45:53
E)51:34
Rationale: C
52:53
Let C.P. of the book be $x.
Then, required ratio = 104% of x / 106% of x
= 104/106 = 52/53 = 52:53
Answer: C
Question: if z=100^2-x^2,then for how many value of x, z is divisible by 6.
Options:
A)33
B)66
C)44
D)55
E)77
Rationale: x can be negative also.
33*2=66
ANSWER:B
Answer: B
Question: In how many ways can the letters of the word ACUMEN be rearranged such that the vowels alwaysappear together?
Options:
A)124 ways
B)144 ways
C)134 ways
D)154 ways
E)164 ways
Rationale: ACUMEN
AUE will come together as a group which can be arranged in 3!=6 ways.
AUE, C,M,N can be arranged in 4!=24 ways.
total possible arrangements = 24*6=144 ways
ANSWER:B
Answer: B
Question: How many cuboids of length 5 m, width 3 m and height 2 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height.
Options:
A)106
B)109
C)108
D)101
E)104
Rationale: (18 × 15 × 12)/(5 × 3 × 2) = 108
Answer is C.
Answer: C
Question: A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
Options:
A)22
B)20
C)99
D)277
E)12
Rationale: x ------- 9
(x + 10) ---- 6
x * 9 = (x + 10)6
x = 20
Answer: B
Answer: B
Question: The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
Options:
A)8, 20, 28
B)16, 28, 36
C)20, 35, 45
D)20, 35, 48
E)None of these
Rationale: Let the present ages are 4x, 7x, 9x.
=> (4x-8) + (7x-8) + (9x-8) = 56
=> 20x = 80
=> x = 4
So their present ages are: 16,28,36
ANSWER:B
Answer: B
Question: The average (arithmetic mean) of six numbers is 5. If 3 is subtracted from each of four of the numbers, what is the new average?
Options:
A)1.5
B)2
C)3
D)4
E)4.5
Rationale: Sum of 6 numbers = 6*5 =30
If 3 is subtracted from each of four of the numbers , we subtract 3*4=12 from the total sum
Sum of 6 number after subtracting 3 from each of four of the numbers = 30 - 12 = 18
New average = 18/6 = 3
Answer C
Answer: C
Question: 9.6 , 9.6 , 10.0 , 10.0 , 10.0 , 10.1 , 10.2 , 10.5
The mean and the standard deviation of the 8 numbers shown above is 10 and 0.278 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?
Options:
A)62.5%
B)85%
C)80.67%
D)75.50%
E)90.30%
Rationale: Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.278; 10+0.278} = {9.722; 10.278}.
From the 8 listed numbers, 5 are within this range so 5/8=62.5%.
Answer: A.
Answer: A
Question: Two different types of tea are mixed, at 6 Kg of type 1 and 4 Kg of type 2. One Kg of type 1 is Rs. 6 and that of type 2 is Rs. 7. The seller get 10% profit, by this action. Find at what price, he had sold the mixture/Kg?
Options:
A)Rs 5.04
B)Rs 7.04
C)Rs 6.04
D)Rs 8.04
E)Rs 9.04
Rationale: CP of 6 kg tea of type 1= 6*6=36 Rs.
CP of 4 kg tea of type 2= 4*7=Rs 28
CP of 10 kg mixed tea = Rs Rs 64
SP of mixture for 10% profit = 64*1.1= Rs 70.4
SP of 1kg mixed tea = Rs 7.04
ANSWER:B
Answer: B
Question: The distance between 2 cities A and B is 1000km. A train starts from A at 12 p.m. and travels towards B at 100 km/hr. Another starts from B at 1 p.m. and travels towards A at 150 km/hr. At what time do they meet?
Options:
A)11am.
B)12p.m.
C)5pm.
D)2p.m.
E)1p.m.
Rationale: Suppose they meet x hrs after 12 p.m.
Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 1000
100x + 150 (x-1) = 1000
x = 4.60 = 5 hrs
They meet at 10+5 = 5 p.m.
Answer is C
Answer: C
Question: If a – b = 3 and a2 + b2 = 29, find the value of ab.
Options:
A)10
B)12
C)15
D)18
E)19
Rationale: EXPLANATION
2ab = (a2 + b2) – (a – b)2
= 29 – 9 = 20
ab = 10.
Answer A
Answer: A