divelab/Sys2Bench huggingface dataset:
Question: A sum of money is to be distributed among A, B, C, D in the proportion of
5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
Options:
A)Rs. 500
B)Rs. 1000
C)Rs. 1500
D)Rs. 2000
E)NOne
Rationale: Sol.
Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 1000 ⇔ x = 1000.
∴ B's share = Rs. 2x= Rs. (2x1000) = Rs. 2000.
Answer D
Answer: D
Question: A drug dealer uses 800gm in place of 1kg to sell his goods. Find his actual % profit or loss, when he sells his article his article on 20% gain on cost price?
Options:
A)32.5%
B)37.5%
C)35%
D)40%
E)50%
Rationale: Selling price of 800gm = 100+20 = $120
Profit = 120-80 = $40
% of profit = 40*100/80 =50 %
Answer is E
Answer: E
Question: The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 4. If the sum of their ages is 88, what is the difference between the ages of Patrick and Monica?
Options:
A)22
B)48
C)45
D)72
E)18
Rationale: Ages of P and Mi=3x:5x
Ages of Mi and Mo=3x:4x
Rationalizing their ages. ratio of their ages will be 9x:15x:20x
Sum=44x=88
x=2
Difference if ages of Pa and Mo=20x-9x=11x=11*2=22
Answer A
Answer: A
Question: Which of the following fractions is greater than 1/10?
Options:
A)1. 12/50
B)2. 3/11
C)3. 2/9
D)4. 4/17
E)5. 6/24
Rationale: 1. 12/50
12.5/50 = 1/4 thus 12/50 < 1/4
2. 3/11
3/12 = 1/4 thus 3/11 > 1/4
3. 2/9
2/8 = 1/4 thus 2/9 < 1/4
4. 4/17
4/16 = 1/4 thus 4/17 < 1/4
5. 6/24
6/24 = 1/4
D
Answer: D
Question: 90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 70% of the total school population of x students, what is x?
Options:
A)113
B)150
C)225
D)250
E)500
Rationale: 90=x/100*70/100*x=>x^2 = 9*10000/7 = > x = 113
A
Answer: A
Question: The circumferences of two circles are 132 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
Options:
A)2996 sq m
B)2897 sq m
C)4312 sq m
D)5768 sq m
E)8470 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 132 and 2∏l = 352
s = 132/2∏ and l = 352/2∏
Difference between the areas = ∏l^2 - ∏s^2
= ∏{66^2/∏^2 - 132^2/∏^2}
= 66^2/∏ - 132^2/∏
= (66 - 132)(66 + 132)/∏
= (110)(242)/(22/7)
= 8470 sq m
Answer:E
Answer: E
Question: If a and b are negative and positive integers respectively,which of the following options must be positive?
Options:
A)ab
B)a/b
C)2a/b
D)4a/b
E)(a + b)^2
Rationale: A. np
-ve*+ve=-ve
will be negative
B. n/p
-ve/+ve=-ve
C.2a/b
-ve/+ve=-ve
D.4a/b
-ve/+ve=-ve
E.(a + b)^2
will be positive irrespective of the absolute values of x and y
will be positive always
Answer: E
Question: In a kilometer race, A beats B by 60 meters or 15 seconds. What time does A take to complete the race?
Options:
A)277 sec
B)235 sec
C)667 sec
D)167 sec
E)176 sec
Rationale: Time taken by B run 1000 meters = (1000 * 15)/60 = 250 sec.
Time taken by A = 250 - 15 = 235 sec.Answer: B
Answer: B
Question: Ayesha's father was 48 years of age when she was born while her mother was 32 years old when her brother six years younger to her was born. What is the difference between the ages of her parents?
Options:
A)22 years
B)24 years
C)26 years
D)28 years
E)29 years
Rationale: Mother's age when Ayesha's brother was born = 32 years.
Father's age when Ayesha's brother was born = (48 + 6) years = 54 years.
Required difference = (54 - 32) years = 22 years. Answer: Option A
Answer: A
Question: A train 400 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)700 m
C)900 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, (400 + x)/60 = 65/3
x = 900 m.
Answer:C
Answer: C
Question: HOW MANY LITRES OF PURE ACID ARE THERE IN 8 LITRES OF A20% SOLUTION?
Options:
A)1.4
B)1.5
C)1.6
D)2.4
E)NONE OF THESE
Rationale: QUANTITY OF PURE ACID=20% OF 8LITRES= (20/100*8)LITRES=1.6 LITRES.
CORRECT OPTIONS:C
Answer: C
Question: In the decimal expansion of (2/5)^8 what is the eighth digit to the right of the decimal point?
Options:
A) 6
B) 5
C) 4
D) 3
E) 2
Rationale: Step 1 Convert fraction to decimal with two decimal places 2/5 = 0.40 then convert to scientific number = 4*10^-1
Step 2 Multiply 4^8 by 10^-8
Step 3 4 has the sequence 4, 16, 64
Answer is A
Answer: A
Question: A and B together can do a work in 5 days. If A alone can do it in 15 days. In how many days can B alone do it?
Options:
A)10
B)99
C)7.5
D)55
E)21
Rationale: 1/5 – 1/15 = 2/15
=> 7.5
Answer: C
Answer: C
Question: Find the average of all the numbers between 6 and 30 which are divisible by 4.
Options:
A)15
B)18
C)20
D)22
E)None
Rationale: Sol.
Average = (8+12+16+20+24+28 / 6) = 108 / 6 = 18
Answer B
Answer: B
Question: What is the sum of this series?
1, 3, 5, 7, 9, ...... 119.
Options:
A)2400
B)1200
C)3600
D)4400
E)2500
Rationale: Number of odd numbers between 1 and 119 is (119+1)/2=60
Therefore Sum of odd numbers 60*60= 3600
ANSWER: C
Answer: C
Question: Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes.
Options:
A)14355
B)15432
C)17576
D)18543
E)16878
Rationale: The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways
The first two letters can chosen in 26 x 26 = 676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
All the three letters can be chosen in 676 x 26 =17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
C
Answer: C
Question: A salesman sold twice as much pears in the afternoon than in the morning. If he sold $480 kilograms of pears that day, how many kilograms did he sell in the afternoon?
Options:
A)120
B)180
C)240
D)280
E)320
Rationale: 3x=480
x=160
Therefore, the salesman sold 160kg in the morning and 2⋅160=320 kg in the afternoon. So answer is E.
Answer: E
Question: The average age of 24 students and the class teacher is 16 years. If the class teacher’s age is excluded, the average reduces by one year. What is the age of the class teacher?
Options:
A)50 years
B)45 years
C)40 years
D)Data inadequate
E)Data inadequate
Rationale: Age of the CT = 25 × 16 – 24 × 15 = 400 – 360 = 40 yrs.
Answer C
Answer: C
Question: A gives B a start of 10 metres in a 100 metre race and still beats him by 1.25 seconds. How long does B take to complete the 100 metre race if A runs at the rate of 10 m/sec?
Options:
A)8 seconds
B)10 seconds
C)16.67 seconds
D)12.5 seconds
E)None
Rationale: Solution:
A gives B a start of 10 metres in a 100 metre race. This means that when A runs 100 metres, B runs only 90 metres.
Despite that start, A beats B by 1.25 seconds.
As A is running at the speed of 10 m/sec, he will take 10 seconds to complete the 100 metre race. And B takes 10 + 1.25 = 11.25 seconds to cover 90 metres.
Therefore, the speed at which B is running = 8 m/sec.
Running at 8 m/sec, B will take = 12.5 seconds to complete the 100 metre race.
Hence the correct answer is D
Answer: D
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
Options:
A)320
B)288
C)322
D)299
E)281
Rationale: Explanation:
Clearly, the numbers are (23 x 13) and (23 x 14).
{\color{Blue} \therefore } Larger number = (23 x 14) = 322.
Answer: C) 322
Answer: C
Question: A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,053. How much did she invest at 5%?
Options:
A)$500
B)$600
C)$700
D)$900
E)$950
Rationale: et x be the portion invested at 5% and
Let (1-x) be the rest which is invested at 6%
The question states that the return after 1 year is (1053/1000)-1 = 0.053 = 5.3%
We want to find the dollar amount invested in X
Using our defined variables, put together the equation and solve for x (the percentage of 1000 invested at 5%)
0.05x+0.06(1-x)= 0.053
(0.05)x +0.06 - (0.06)x = 0.053
-0.01x = -0.007
x= -0.007/-0.01 = 7/10 = 70%
So X = 70% of the 1000 which is 700
ANSWER:C
Answer: C
Question: In a class of 60 children, 30% children can speak only English, 20 % Hindi and English both and the rest of the children can speak only Hindi. How many children can speak Hindi?
Options:
A)42
B)36
C)30
D)48
E)None of these
Rationale: Number of students who speak only English
= 30% of 60 = 18
∵ Number of students who speak Hindi and English
= 20% of 60 = 12
∵ Number of students who speak only Hindi
= (60 – 30 =) 30
∵ No. of students who speak Hindi = 30 + 12 = 42
Answer A
Answer: A
Question: I chose a number and divide it by 8. Then I subtracted 100 from the result and got 6. What was the number I chose?
Options:
A)600
B)700
C)800
D)900
E)848
Rationale: Solution:
Let x be the number I chose, then
x/8âˆ’100=6
x/8=106
x=848
Answer E
Answer: E
Question: In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure how many draws did it take before the person picked a heart and won. What is the probability that there will be at least three draws involved in a win, i.e. someone picking her first heart on the third draw or later?
Options:
A)1/2
B)9/16
C)11/16
D)13/16
E)15/16
Rationale: Probability of picking a heart on any draw = 1/4
Probability of NOT picking a heart on the first draw AND on the second draw = [1-(1/4)] X [1-(1/4)] = 3/4 X 3/4 = 9/16
Answer:B
Answer: B
Question: A train moves with a speed of 135 kmph. Its speed in metres per second is
Options:
A)10.8
B)37.5
C)30
D)38.8
E)None
Rationale: Solution
Speed	= 135Kmph
= (135x 5/18)m/sec
= 37.5 m/sec.
Answer B
Answer: B
Question: Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 2 to 8. If a total of 120 sandwiches were made, how many bologna sandwiches
were made?
Options:
A)16
B)30
C)38
D)42
E)48
Rationale: For deciding such task we should calculate all parts 5 + 2 + 8 = 15 parts
and we should calculate how many sandwiches holds 1 part:
120 / 15 =6 sandwiches in one part
For bologna we have 7 parts so:
2 * 8=16
Answer is A
Answer: A
Question: A Colmar's train rails across an open track at 250 kilometers per hour. A regular passenger train travels at 68% of the Colmar's train speed. If the two trains start moving from the same station at the same time, how much time longer will it take the passenger train than the Colmar's to travel 850 kilometers?
Options:
A)1 hour and 24 minutes.
B)1 hour and 36 minutes.
C)2 hours and 24 minutes.
D)2 hours and 36 minutes.
E)5 hours.
Rationale: Difference in time = time taken by passenger train- time taken by Colmar's train
850/(250*68) *100 - 850/250
850 (100/ 250*68 - 1/250)
850*32/ (250*68)
1.6 hrs or 1 hr and 36 mins
B is the answer
Answer: B
Question: If m is the average (arithmetic mean) of the first 10 positive multiples of 2 and if M is the median of the first 10 positive multiples of 2, what is the value of M – m ?
Options:
A) –5
B) 0
C) 5
D) 25
E) 27.5
Rationale: The first 10 positive multiples of 2 is an evenly spaced set. One of the most important properties of evenly spaced set (aka arithmetic progression) is:in any evenly spaced set the arithmetic mean (average) is equal to the median.
Hence M=m --> M-m=0.
Answer: B.
Answer: B
Question: If A = x% of y and B = y% of x, then which of the following is true?
Options:
A)A is greater than B
B)A is smaller than B.
C)None of these
D)A is Equal to B
E)Relationship between A and B cannot be determined.
Rationale: x% of y = (x/100 x y) = (y/100 x x) = y% of x
A = B.
answer :D
Answer: D
Question: The average age of a class of 42 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
Options:
A)30 Years
B)31 Years
C)32 Years
D)34 Years
E)59 Years
Rationale: Total age of students is 42X16 = 672 Years
Total age inclusive of teacher = 43X (16+1) = 731
So, Teacher's age is 731-672 = 59 Yrs
There is a shortcut for these type of problems
Teacher's age is 16+(43X1) = 59 Years
E
Answer: E
Question: After an English exam, 9 percent of the test takers reported that they didn't study, while 10 percent of the test takers who didn't study refused to admit they hadn't studied. What percent of the test takers didn't study?
Options:
A)9%
B)25%
C)80%
D)10%
E)60%
Rationale: Statement: 9% of Test Takers (TT) Reported they Didn't Study (RDS). Of the test takers who didn't study (DS) 10% refused to admit they didn't study (notRDT). [Note: A Venn Diagram is useful to visualize the problem.]
Solution: Sample space is 100%.
TT = 100%
RDS/TT = 9%
notRDS/DS = 10% => 100% - 10% => RDS/DS = 90%
DS/TT = (9)/(90)% = 10%
Answer: D
Answer: D
Question: A city council will select 2 of 6 available firefighters and 1 of 6 available police officers to serve on an advisory panel. How many different groups of 3 could serve on the panel?
Options:
A)36
B)90
C)144
D)216
E)432
Rationale: OA D
6C2 * 6C1
using the combination formula to choose 2 from 9 and 1 from 6
B
Answer: B
Question: If 40% of a certain number is 160, then what is 10% of that number?
Options:
A)100
B)40
C)80
D)120
E)110
Rationale: Explanation:
40% = 40*4 = 160
10% = 10*4 = 40
Answer: Option B
Answer: B
Question: A bank pays interest to its customers on the last day of the year. The interest paid to a customer
is calculated as 10% of the average monthly balance maintained by the customer. John is a
customer at the bank. On the last day, when the interest was accumulated into his account, his
bank balance doubled to $1710. What is the average monthly balance maintained by John in his
account during the year?
Options:
A)2840
B)5680
C)6840
D)8550
E)28400
Rationale: Soln:-
Bank balance is doubled with accumulation of interest to 1710..
this means INTEREST is 1710/2=855 for entire year..
although since interest is 10% of avg MONthly balance, it becomes 8550..
ANSWER:D
Answer: D
Question: When the no.7y86038 is exactly divisible by 11, then the smallest whole no.in place of y?
Options:
A)1
B)2
C)3
D)5
E)6
Rationale: The given number =7y86038
Sum of the odd places =8+0+8+7=23
Sum of the even places = 3+6+y
(Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)
23-(9+y) = divisible by 11
14 � y = divisible by 11.
Y must be 3, to make given number divisible by 11.
C
Answer: C
Question: 18 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
Options:
A)230
B)274
C)306
D)354
E)424
Rationale: 2*18C2 = 2*153 = 306
The answer is C.
Answer: C
Question: At the end of the first quarter, the share price of a certain mutual fund was 25 percent higher than it was at the beginning of the year. At the end of the second quarter, the share price was 80 percent higher than it was at the beginning of the year. What was the percent increase in the share price from the end of the first quarter to the end of the second quarter?
Options:
A)20%
B)25%
C)30%
D)33%
E)44%
Rationale: Another method is to use the formula for 2 successive percentage changes:
Total = a + b + ab/100
80 = 25 + b + 25b/100
b = 44
Answer (E)
Answer: E
Question: Find a sum for first 10 prime no's from number series?
Options:
A)24
B)28
C)129
D)178
E)140
Rationale: Required sum = (2+ 3+ 5+ 7+11+ 13+17+ 19+23+ 29) = 129
Note: 1 is not a prime number
Option C
Answer: C
Question: A merchant has selected two items to be placed on sale, one of which currently sells for 45 percent less than the other. If he wishes to raise the price of the cheaper item so that the two items are equally priced, by what percentage must he raise the price of the less expensive item?
Options:
A)100 %
B)90%
C)80%
D)70%
E)60%
Rationale: Expensive item = $100;
Cheap item = $55;
We must increase $55 to $100, so by $45, which is approximately 80% increase: (100-55)/55 = 3/7 = ~0.81.
Answer: C.
Answer: C
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
Options:
A)18 m
B)17 m
C)27 m
D)28 m
E)29 m
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.
Answer: B
Answer: B
Question: A no.when divided by 281 gives a remainder 160, what remainder will be obtainedby dividingthe same no.21?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: 281 + 160 = 441/21 = 21 (Remainder)
A
Answer: A
Question: A certain child ate the following number of grapes on each of five days: 15, 19, 23, 26, 30. If the child were to have eaten 10 more grapes on the day she ate the most grapes, which of the following statements best describes the change in the mean and the median number of grapes?
Options:
A) The mean and the median will remain unchanged.
B) The mean will remain unchanged but the median will increase.
C) The mean will increase but the median will remain unchanged.
D) The mean and the median will increase by the same amount.
E) The mean and the median will increase by different amounts.
Rationale: Old set = {15, 19, 23, 26, 30}.
New set = {15, 19, 23, 26, 40} --> the median (middle term) will remain the same and the mean will increase.
Answer: C.
Answer: C
Question: If log1087.5 = 1.9421, then the number of digits in (875)10 is?
Options:
A)30
B)28
C)27
D)26
E)25
Rationale: X = (875)10 = (87.5 x 10)10
Therefore, log10X = 10(log1087.5 + 1)
= 10(1.9421 + 1)
= 10(2.9421) = 29.421
X = antilog(29.421)
Therefore, number of digits in X = 30.
ANSWER:A
Answer: A
Question: A train is 357 meter long is running at a speed of 42 km/hour. In what time will it pass a bridge of 137 meter length?
Options:
A)44
B)42.343
C)50
D)39.252
E)27.851
Rationale: Speed = 42 Km/hr = 42*(5/18) m/sec = 35/3 m/sec
Total distance = 357+137 = 494 meter
Time = Distance/speed
= 494 * (3/35) = 42.343 seconds.
Answer: B
Answer: B
Question: 96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
Options:
A)49
B)40
C)42
D)66
E)44
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 96 = 42
Answer: C
Answer: C
Question: If $10 be allowed as true discount on a bill of $110 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is:
Options:
A)$18.33
B)$22.33
C)$28.33
D)$26.23
E)$16.23
Rationale: S.I. on $ (110 - 10) for a certain time = $10.
S.I. on $ 100 for double the time = $20.
T.D. on $ 120 = $ (120 - 100) =$20.
T.D. on $ 110 = $ (20/120 * 100)= $18.33
ANSWER:A
Answer: A
Question: For 1rs 4p interest
wat will be for 5000rs?
Options:
A)350Rs
B)450Rs
C)200Rs
D)30Rs
E)448Rs
Rationale: For 1rs , 4p interest
for 5000rs, x
x= 5000/1 * 4p ==> 20000 paise
To express in rs, 20000/100 = 200rs
ANSWER:C
Answer: C
Question: John purchased n items from a catalog for $16 each. Postage and handling charges consisted of $9 for the first item and $5 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?
Options:
A)17n + 2
B)17n + 4
C)19n + 2
D)19n + 3
E)19n + 4
Rationale: its B
n items for $16 each
total price $16n
postage and handling of $9 for 1st item and $5 for the rest
total postage and handling = $ [9+ (n-5)]
= $ 16+4
total cost
16n+n+4 = 17n+4
Answer: B
Question: In how many different ways can the letters of the word ‘PREPTY’ be arranged?
Options:
A)280
B)290
C)300
D)340
E)360
Rationale: Number of ways = 61/21 6X5X4X3X2X1 - 360
E
Answer: E
Question: On a game show, a contestant spins three four wheels; each wheel is numbered 1 to 7. What is the probability that the contestant will spin all tens?
Options:
A)1/2401
B)2/5
C)1
D)9
E)63
Rationale: All 7s:
1st wheel = 7= 1/7
2nd wheel = 7 = 1/7
3rd wheel = 7 = 1/7
4th wheel = 7 = 1/7
(1/7)(1/7)(1/7)(1/7) = 1/2401
Answer: A
Answer: A
Question: The L.C.M of 23 * 32 * 5 and 33 * 5 2 * 23 is.
Options:
A)22 * 32 * 5
B)23 * 33 * 52
C)23 * 5 * 32
D)23 * 32 * 5
E)None of these
Rationale: The L.C.M of 23 * 32 * 5 and 33 * 5 2 * 23 is
23 * 33 * 52
ANSWER:B
Answer: B
Question: Patrick put together an indoor soccer team. Only 5 people play at a time. There are 10 people on the team. How many different line-ups can Patrick send out on the field?
Options:
A)56
B)202
C)252
D)402
E)424
Rationale: Combination calc is: n C r = n! /(r!*(n-r)!) 10 P 5 = 10!/(5!x(10-5)!) = 10x9x8x7x6x(5x4x3x2x1)/(5!x5!)=10x9x8x7x6/(5x4x3x2x1)=252 Correct answer is C (252)
Answer: C
Question: A waitress's income consists of her salary and tips.During one week ,her tips were 3/4 of her salary.What fraction of her income for the week came from tips?
Options:
A)1/9
B)1/6
C)3/7
D)4/9
E)5/9
Rationale: Her tips were 3/4 of her salary.
Let's say her salary =$4
This mean her tips = (3/4)($4) =$3
So, her TOTAL INCOME =$4+$3=$7
What fraction of her income for the week came from tips
$3/$7= 3/7
= C
Answer: C
Question: Irin, Ingrid and Nell bake chocolate chip cookies in the ratio of 9.18: 5.17: 2.05. If altogether they baked a batch of 148 cookies, what percent of the cookies did Ingrid bake?
Options:
A)0.125%
B)1.25%
C)12.5%
D)30%
E)0.352%
Rationale: 9.18x+5.17x+2.05x = 16.4x = 170 cookies
x= 170/16.4 = 10 (approx)
So, Ingrid baked 10*5.17 cookies or 51 cookies (approx)
% share = 51/170 =30 approx
Hence, answer is D.
Answer: D
Question: A man can row upstream at 8kmph and downstream at 13 kmph.The speed of the stream is :
Options:
A)2.5 km/hr
B)4.2 km/hr
C)5 km/hr
D)10.5 km/hr
E)None of these
Rationale: Solution
Speed of stream =1/2(13-8) kmph = 2.5 kmph . Answer A
Answer: A
Question: In an examination, 32% of total students failed in Hindi, 56% failed in English and 12% in both. The percentage of these who passed in both the subjects is :
Options:
A)24
B)37
C)28
D)40
E)81
Rationale: Explanation:
Formula n(aâˆªb) = n(a) + n(b) âˆ’ n(aâˆ©b)
Fail in Hindi or English = 32 + 56 â€“ 12 = 76
Therefore students who passed = 100 â€“ 76 = 24.
Answer: A
Answer: A
Question: There are between 200 and 210 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?
Options:
A) 201
B) 203
C) 206
D) 210
E) 209
Rationale: Let number of cards = x
If the cards are counted 3 at a time , there are 2 left over-
x= 3p+2
x can take values 201 , 206
If the cards are counted 4 at a time , there is 1 left over
x= 4q+1
x can take values 201 , 208
Therefore , x = 201
Answer A
Answer: A
Question: Find the sum of the number of combinations possible by using 1,2,3,4 such that no number is repeated(ex:- 1223,4322 are invalid 1234,4321 are valid)more than once.
Options:
A)66660
B)66760
C)66860
D)66960
E)67660
Rationale: total no. formed = 4!=4*3*2*1=24
each digit will be used at each positions, 6 times
sum of digits at unit place = 6*1+6*2+6*3+6*4 = 6*(1+2+3+4)= 60
this sum will be same for hundred, tens & unit places
sum of all 4 digit numbers formed using digits 1,2,3,4
= 1000*60+100*60+10*60+60
=60*(1000+100+10+1)
=60*1111
=66660
ANSWER:A
Answer: A
Question: A meeting has to be conducted with 5 employees.Find the number of ways in which the employees may be selected from among 9 employees,if 2 employees will not attend the meeting together.
Options:
A)1.35
B)2.12
C)3.91
D)4.126
E)5.15
Rationale: 9 employees, but two of them cannot attend the meeting together.
We can split it into two cases.
1. Meeting without these two employees in it. That would mean selecting 5, from the remaining 7 which is 7C5 = 21
2. Meeting with one of the two employees. select 1 manager from two, and then select 4 from the remaining 7, which is 2C1 X 7C4 = 70.
So, answer is 21 + 70 = 91.
Answer : C
Answer: C