divelab/Sys2Bench huggingface dataset:
Question: Out of n consecutive natural numbers, four numbers are selected such that the differences of all the possible pairs are distinct. What is the least value of n for which this is possible?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: Explanation :
Let the 4 numbers be X1, X2, X3, X4 where X1<X2<X3<X4. Let X1 + a1 = X2, X2 + a2 = X3, X3 + a3 = X4. The difference of X1 and each of the other three, of X2 and each of the greater two, of X3 and X4 are tabulated.
X1	X2	X3
X2	a1
X3	a1+a2	a2
X4	a1+a2+a3	a2+a3	a3
We require that n be minimized and these 6 expressions have distinct values. Let X1 = 1
Now, n = 1+a1+a2+a3. Now a1, a2, a3 can be chosen as the least possible values i.e. 1,2 and 3. However the order of chosing should be such that the six expressions (differences) should all be distinct.
By little trial and error (a1, a2, a3) can be (1, 3, 2) or (2, 3, 1) in which case n = 7 and the four numbers can be (1, 2, 5, 7) or (1, 3, 6, 7) respectively.
Hence the minimum value of n is 7.
Answer : B
Answer: B
Question: A pipe takes a hours to fill the tank. But because of a leakage it took 5 times of its original time. Find the time taken by the leakage to empty the tank
Options:
A)50 min
B)60 min
C)90 min
D)80 min
E)75 min
Rationale: pipe a can do a work 60 min.
lets leakage time is x;
then
1/60 -1/x=1/300
x=75 min
ANSWER:E
Answer: E
Question: A person is traveling at 65 km/hr and reached his destiny in 3 hr then find the distance?
Options:
A)205 km
B)195 km
C)295 km
D)115 km
E)215 km
Rationale: T = 3 hrs
D= T*S = 65*3 = 195 km
Answer is B
Answer: B
Question: The number of boys in the class is 8 more than the number of girls in the class, which is five times the difference between the number of girls and boys in the class.How many boys are there in the class?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: 8+y=5(x-y); y=no of girlz & x=boys
so, y=32 & x=8+y ie 40
40 ans.
ANSWER:C
Answer: C
Question: If it is a 3x3 matrix, for which elements in first row are (V, 50, W), second row (196,X, Y)and in third row are (269, Z, 123).It is given that the sum of the numbers in each row, column, diagonal are same. Then find the value of (Y + Z).
Options:
A)1118
B)1119
C)1121
D)1122
E)1144
Rationale: matrix
v 50 w
196 x y
269 z 123
in 1st row and 1st column
v+196+269=v+50+w
w=415
Again, in 2nd column and 3rd row
50+x+z=269+z+123
x=342
As sum of each row column and diagonal are same.
So, 269+342+415=1026
415+y+123=1026
y=488
269+z+123=1026
z=634
y+z=488+634=1122
ANSWER:D
Answer: D
Question: Solve 8x – 4 = 4x + 11
Options:
A)5(1/3)
B)6(1/3)
C)7(1/3)
D)3(3/4)
E)9(1/3)
Rationale: Sol.
8x – 4 = 4x + 11
=> 8x – 4x = 11 + 4
=> 4x = 15 => x = 15/3 = 3(3/4).
Answer D
Answer: D
Question: 3,4,7,11,18,29,47,?
Options:
A)76
B)77
C)75
D)78
E)79
Rationale: Each number is the sum of the previous two numbers, ie 29 + 47 = 76.
Answer : A
Answer: A
Question: The greatest number of four digits which is divisible by 10, 20, 25 and 60 is:
Options:
A)9000
B)9300
C)9400
D)9600
E)9700
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 10, 20, 25 and 60 is 1500.
On dividing 9999 by 1500, the remainder is 999.
Required number (9999 - 999) = 9000.
ANSWER :A
Answer: A
Question: A company, Chauncy Co., has an annual travel budget of $59,000. The accounting department estimates that transportation expenses will increase 5 percent in the coming year, and nontransportation travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent $19,500 on transportation-related expenses, and $35,000 on nontransportation travel expenses. If the annual travel budget does not increase this year, and if the accounting department’s estimates are correct, how far over the annual travel budget will expenses be this year?
Options:
A)Expenses will not go over the budget.
B)$500
C)$4,225
D)$1,725
E)$60,725
Rationale: annual travel budget of $59,000
Let, Transportation expenses = T = 19500
and Non-Transportation expenses = N=35000
i.e. Increased Transportation expenses = 1.05T = 20475
and Increased Non-Transportation expenses = 1.15N = 40250
Total Expense = 20475+40250 = 60725
Expense over Budget = Budget - expense = 59000-60725 = 1725
Answer: Option D
Answer: D
Question: If each term in the sum a1+a2+a3+.....+an is either 7 or 77 and the sum equals 343, which of the following could be equal to n?
Options:
A)38
B)39
C)40
D)41
E)42
Rationale: Since, there is no 49 in the answer choices (343/7 = 49), we know there is at least one 77.
343 - 77 = 266
266/7 = 38
38+1 = 39.
If 39 wasn't there, I would have subtracted 77 from 266 and continued in a similar way.
Ans.B
Answer: B
Question: Company P had 15 percent more employees in December than it had in January. If Company P had 470 employees in December, how many employees did it have in January?
Options:
A) 391
B) 408
C) 410
D) 423
E) 445
Rationale: D = number of employees in December
J = number of employees in January
J x 1.15 = D
J x 1.15 = 470
J = 470/1.15
J = 47,000/115 = 408
Thus B is the correct answer.
Answer: B
Question: Two men and three women working 7 hours a day finish a work in 5 days. Four men and four women working 3 hours a day complete the work in 7 days. The number of days in which only 7 men working 4 hours a day will finish the work is?
Options:
A)5
B)6
C)1
D)7
E)8
Rationale: 2M + 3W ----- 35 h
4M + 4W ------- 21 h
7M -------? d
70M + 105W = 84M +84M
21W = 14M => 2M = 3W
4 * 35 = 7 * x => x = 20 hours
20/4 = 5 days
Answer: A
Answer: A
Question: If log 2= 0.030103, the number of digits in 264 is :
Options:
A)18
B)19
C)20
D)21
E)22
Rationale: log 264 = 64 log 2 = (64*0.30103) = 1926592
Its characteristics is 19.
Hence, the number of digits in 264 is 20.
ANSWER:C
Answer: C
Question: If air is called green , green is called blue, blue is called orange, sky is called yellow, yellow is called water and water is called pink, then what is the color of clear sky ?
Options:
A)Orange
B)Sky
C)Water
D)Yellow
E)Black
Rationale: Explanation:The colour of clear sky is 'blue' and as given, 'blue' is called 'orange'.So, the colour of clear sky is 'orange'.Answer: A
Answer: A
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.12000. A's share is?
Options:
A)8876
B)2765
C)4000
D)1298
E)1261
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 12000 = 4000
Answer:C
Answer: C
Question: In a panel of 10 light bulbs, the odds of any light bulb to burn out are 0.7 at any given 10 minutes. Should a light bulb burn out, the whole panel would instantly turn off. What are the odds that the panel would be turned off within the first 10 minutes after it was switched on?
Options:
A)1-0.06^10
B)1-0.3^10
C)(1-0.3)^10
D)0.06
E)1-10*0.06
Rationale: ans B.
Prob that light will not turned off = 0.3^10. Hence prob (turn off) = 1 - prob (not turn off).
Answer: B
Question: Winona can purchase a pencil and two pens for 250 cents, or two pencils and three pens for 425
cents. If the cost of a pencil and the cost of a pen does not change, compute the cost in cents
of FIve pencils and six pens.
Options:
A)550 cents.
B)650 cents.
C)750 cents.
D)850 cents.
E)950 cents.
Rationale: If we add one pencil and one pen, an order increases in price by 175 cents. Therefore,
adding four pencils and four pens increases the order by 700 cents, so the cost of five pencils
and six pens is 700 + 250 = 950 cents.
correct answer E
Answer: E
Question: A tap can fill a tank in 10 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?
Options:
A)5 hrs 15 mins
B)11 hrs 15 mins
C)3 hrs 15 mins
D)6 hrs 15 mins
E)7 hrs 15 mins
Rationale: Time taken by one tap to fill the tank = 5 hrs.
Part filled by the taps in 1 hour = 4 * 1/10 = 2/5
Remaining part = 1 - 1/2 = 1/2
2/5 : 1/2 :: 1 : x
x = 1/2 * 1 * 5/2 = 5/4 = 1 hr 15 mins
So, total time taken = 11 hrs 15 mins
ANSWER: B
Answer: B
Question: A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.2662 in 3 years. Find the rate percent?
Options:
A)30%
B)10%
C)20%
D)19%
E)50%
Rationale: 2420 --- 242
100 --- ? => 10%
Answer: B
Answer: B
Question: In a card game, a combination of three kings beats all others. If Jose is the first to draw from a standard deck of 52 cards, what is the probability that he wins the game with the best possible combination?
Options:
A)1/5550
B)1/5600
C)1/5400
D)1/5525
E)1/5425
Rationale: he best possible combination is the case when he wins in his first two draws
There are 52 cards in a deck of cards with 4 kings in it.
Probability of first card to be king = 4/52
Probability of Second card to be king = 3/51
Probability of third card to be king = 2/50
Probability of Best possible case = (4/52)*(3/51)*(2/50) = 1/5525
D
Answer: D
Question: Two trains travelling in the same direction at 40 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 125 m, what is the length of the second train?
Options:
A)228
B)266
C)175
D)99
E)171
Rationale: RS = 40 – 22 = 18 * 5/18 = 5 mps
T = 60 sec
D = 5 * 60 = 300 m
125
--------
175 m
Answer: C
Answer: C
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is?
Options:
A)650
B)690
C)698
D)700
E)710
Rationale: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698.
Answer: Option C
Answer: C
Question: A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?
Options:
A)100
B)400
C)300
D)500
E)700
Rationale: Explanation :
Amount of work A can do in 1 day = 1/6
Amount of work B can do in 1 day = 1/8
Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24
Amount of work A + B + C can do = 1/3
Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24
work A can do in 1 day: work B can do in 1 day: work C can do in 1 day
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1
Amount to be paid to C = 3200 × (1/8) = 400
ANSWER:B
Answer: B
Question: A man has Rs.355 in the denominations of one-rupee notes, 20-rupee notes and 50-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)20
B)15
C)71
D)40
E)60
Rationale: Let number of notes of each denomination be x.
Then x + 20x + 50x = 355
71x = 355
x = 5
Hence, total number of notes = 3x = 15.
Answer is B.
Answer: B
Question: If √10 = 3.16, find the value of If √5/2
Options:
A)1.3
B)1.58
C)2.03
D)2.15
E)None of these
Rationale: Explanation:
√(5/2) =√(5×2/2×2)= √(10)/2 =3.16/2 = 1.58
ANSWER: B
Answer: B
Question: What should come in place of the question mark (?) in the following equation?
6000 + 500 = 870+ ?
Options:
A)6789
B)3654
C)5630
D)6777
E)1298
Rationale: 6000 + 500 = 870+ ?
6000 + 500 – 870= 5630
Answer C
Answer: C
Question: If daily wages of a man is double to that of a woman, how many men should work for 10 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.
Options:
A)12
B)14
C)16
D)20
E)40
Rationale: Explanation :
Wages of 1 woman for 1 day = 21600/40Ã—30
Wages of 1 man for 1 day = 21600Ã—2/40Ã—30
Wages of 1 man for 10 days = 21600Ã—2Ã—10/40Ã—30
Number of men = 14400/(21600Ã—2Ã—10/40Ã—30)=144/(216Ã—20/40Ã—30)=40
Answer : Option E
Answer: E
Question: A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely ?
Options:
A)6 min to empty
B)7 min to full
C)6 min to full
D)7 min to empty
E)None of these
Rationale: Explanation:
There are two important points to learn in this type of question,
First, if both will open then tank will be empty first.
Second most important thing is,
If we are calculating filling of tank then we will subtract as (filling-empting)
If we are calculating empting of thank then we will subtract as (empting-filling)
So lets come on the question now,
Part to emptied 2/5
Part emptied in 1 minute = 1/6-1/10=1/15
=>1/15:2/5::1:x
=>2/5âˆ—15=6mins
ANSWER IS A
Answer: A
Question: In a class of 30 students, 5 students did not borrow any books from the library, 10 students each borrowed 1 book, 8 students each borrowed 2 books, and the rest of the students each borrowed at least 4 books. If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed ?
Options:
A)5
B)8
C)16
D)18
E)20
Rationale: The average number of books per student was 2means that total of 2*30=60 books were borrowed;
5+12+8=25 students borrowed total of 5*0+12*1+8*2=28 books;
So 60-28=32 books are left to distribute among 30-25=5 students, these 5 arethe rest who borrowed at least 4 books;
Tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed. Minimum these 4 students could have borrowed is 4 books per student, so total number of books they could have borrowed is 4*4=16 books. So the 5th student could have borrowed is 32-16=16 books.
Answer: C.
Answer: C
Question: The L.C.M of two numbers is 45 times their H.C.F if one of the numbers is 125and sum of H.C.F and L.C.M. is 1150, the other number is:
Options:
A)215
B)220
C)225
D)235
E)none of these
Rationale: Let H.C.F be h and L.CM be l.Then, l-45h and l+h=1150
45h+h=1150 or h=25.so, l=(1150-25)-1125.
Hence, other number=(25*1125/125)=225.
Correct Option:C
Answer: C
Question: A two member committee comprising of one male and one female member is to be constitute out of five males and three females. Amongst the females. Ms. A refuses to be a member of the committee in which Mr. B is taken as the member. In how many different ways can the committee be constituted ?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: Solution: 5C1 * 3C1 -1
= 15-1
= 14
Answer: Option D
Answer: D
Question: A man on tour travels first 160 km at 64 km/he and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is?
Options:
A)71.17 km/hr
B)71.21 km/hr
C)71.11 km/hr
D)81.11 km/hr
E)77.11 km/hr
Rationale: Total time taken = (160/64 + 160/8) = 9/2 hrs.
Average speed = 320 * 2/9 = 71.11 km/hr.
Answer:C
Answer: C
Question: Mohit sold an article for Rs. 18000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
Options:
A)Rs.15000
B)15002
C)26879
D)26992
E)12681
Rationale: Let the CP be Rs. x.
Had he offered 10% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x
= Rs. 1.08x = 18000 - 10/100(18000)
= 18000 - 1800 = Rs. 16200
=> 1.08x = 16200
=> x = 15000
Answer: A
Answer: A
Question: A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 25 days starting with sunday is
Options:
A)342
B)285
C)290
D)295
E)275
Rationale: Explanation:
As the month begin with sunday, so there will be five sundays in the month. So result will be:
=(510×5+240×25/30)=(8550/25)=342
Answer: Option A
Answer: A
Question: How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg?
Options:
A)36 kg
B)42 kg
C)54 kg
D)63 kg
E)30 kg
Rationale: Explanation:
S.P. of 1 kg of mixture = Rs. 9.24, Gain 10%.
C.P. of 1 kg of mixture = Rs.(100/110 x 9.24)= Rs. 8.40
By the rule of allilation, we have:
Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.
Let x kg of sugar of 1st be mixed with 27 kg of 2nd kind.
Then, 7 : 3 = x : 27
x =(7x 27 / 3)= 63 kg.
ANSWER IS D
Answer: D
Question: The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?
Options:
A)1/2
B)3/4
C)3/5
D)3/7
E)4/9
Rationale: Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D
1 2 3 1 =iXiX71=4;
1 3 Required probability 3/4
B
Answer: B
Question: What is the average (arithmetic mean) of all the multiples of ten from 10 to 170 inclusive?
Options:
A)90
B)80
C)100
D)105
E)110
Rationale: 10 and 190 inclusive would mean there are 17 terms.
No need to add up all the terms and further divide by 17 since the terms are evenly spaced in ascending order from 10, 20, 30........170
The middle term is the average which is the tenth term = 80
B is the answer.
Answer: B
Question: Pipe A can fill a tank in 9 hours, pipe B in 12 hours, and pipe C in 18 hours. If all the pipes are open, in how many hours will the tank be filled?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: The part filled by A + B + C in 1 hour
= 1/9 + 1/12 + 1/18
= 9/36 = 1/4
All the three pipes together will fill the tank in 4 hours.
The answer is C.
Answer: C
Question: A bartender removed from a bottle a certain quantity of a drink which had 25 % ALCOHOL CONTENT and replaced the same quantity with another drink that had an alcohol content of 10%. The alcohol content in the drink after replacement is 20 % What the quantity of the drink that he replaced if there was 1 Litres of the drink in the bottle
Options:
A)1/2
B)1/3
C)2/3
D)3/5
E)5/8
Rationale: 1 litre of drink = 1000 milliliters
Let x be the quantity taken out
We now have 1000 - x quantity of liquid => there is 0.25(1000-x) quantity of alcohol. --- (1)
Now, we add x amount of alcohol from a 10% concentrate. It means 0.1x alcohol is added ---(2)
Since it says final alcohol content in 1 litre of drink is 20% or 200 milli litre
from (1) and (2) above -
(1000-x)0.25 + 0.1x = 200
Solving for x, we get 333.33 ml or 1/3 of a litre
ANSWER:B
Answer: B
Question: There are 200 questions in a 3 hr examination. Among these questions there are 50 mathematics problems. It is suggested that twice as much time be spent on each maths problem as for each other question. How many minutes should be spent on mathematics problems
Options:
A)36 minutes
B)60 minutes
C)72 minutes
D)100 minutes
E)None of these
Rationale: Explanation :
Let x = minutes spent on a non-math problem
then 2x = minutes spent on a math problem
x(200-50) + 2x(50) = 180
x(150) + 2x(50) = 180
150x + 100x = 180
250x = 180
x = 0.72 minutes
Time to spend on math problems:
2x(50)=100x = 100(0.72) = 72 minutes
Answer : C
Answer: C
Question: The Income of a man increase consistently by 2% per year. If his present income is Rs. 12000 then what will his income be after 1 year ?
Options:
A)12040
B)12140
C)12240
D)12340
E)12440
Rationale: Explanation :
Income = 12000 x 1.02 = 12240
Answer : Option C
Answer: C
Question: Two men started from the same place walk at the rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5 km apart, if they walk in the same direction?
Options:
A)10hours
B)12hours
C)17hours
D)15hours
E)20hours
Rationale: To be 0.5km apart they take 1 hour
To be 8.5km apart they take = 1/0.5 * 8.5 = 17 hours
Answer is C
Answer: C
Question: What distance (in meters) will be covered by a bus moving at 54 km/hr in 30 seconds?
Options:
A)390
B)420
C)450
D)480
E)510
Rationale: 54 km/hr = 54 * 5/18 = 15 m/s
distance = 15 * 30 = 450 meters
The answer is C.
Answer: C
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1800. The difference between the profit shares of A and C is?
Options:
A)720
B)266
C)155
D)600
E)441
Rationale: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1800
=> 5 parts out of 15 parts is Rs. 1800
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1800) = Rs. 720
Answer:A
Answer: A
Question: A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 10 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate?
Options:
A) 3/8
B) 9/10
C) 1/2
D) 3/5
E) 3/4
Rationale: x * 6/100 * 1 + (20000 - x) * 10/100 * 1 = 1440
6x - 8x = 144000 - 200000
=> -2x = -4000
=> x = 2000
So 18000/20000 = 9/10
Answer - B
Answer: B
Question: The sale price sarees listed for Rs.400 after successive discount is 25% and 20% is?
Options:
A)297
B)879
C)342
D)240
E)269
Rationale: 400*(75/100)*(80/100)
= 240
Answer: D
Answer: D
Question: A bus travels from town A to town B. If the bus's speed is 50 km/hr, it will arrive in town B 42 min later than scheduled. If the bus increases its speed by 509509 m/sec, it will arrive in town B 30 min earlier than scheduled. Find:
A) The distance between the two towns;
B) The bus's scheduled time of arrival in B;
C) The speed of the bus when it's on schedule.
Options:
A)60
B)37
C)26
D)28
E)11
Rationale: First we will determine the speed of the bus following its increase. The speed is increased by 509509 m/sec =50⋅60⋅6091000=50⋅60⋅6091000 km/hr =20=20 km/hr. Therefore, the new speed is V=50+20=70V=50+20=70 km/hr. If xx is the number of hours according to the schedule, then at the speed of 50 km/hr the bus travels from A to B within (x+4260)(x+4260) hr. When the speed of the bus is V=70V=70 km/hr, the travel time is x−3060x−3060 hr. Then
50(x+4260)=70(x−3060)50(x+4260)=70(x−3060)
5(x+710)=7(x−12)5(x+710)=7(x−12)
72+72=7x−5x72+72=7x−5x
2x=72x=7
x=72x=72 hr.
So, the bus is scheduled to make the trip in 33 hr 3030 min.
The distance between the two towns is 70(72−12)=70⋅3=21070(72−12)=70⋅3=210 km and the scheduled speed is 210/7/2=60 km/hr.
Answer:A
Answer: A
Question: If x = |x| , then which one of the following statements could be true?
I. x = 0
II. x < 0
III. x > 0
Options:
A) None
B) I only
C) III only
D) I and II and III
E) II and III
Rationale: Answer copied from NOVA guide
Statement I could be true because ± 0 = −(+0) = −(0) = 0 .
Statement II could be true because the right side of the equation is always negative [ ± x = (a positive number) = a negative number].
Now, if one side of an equation is always negative, then the other side must always be negative,
otherwise the opposite sides of the equation would not be equal.
Since Statement III is the opposite of Statement II, it must be false. But let’s show this explicitly:
Suppose x were positive. Then x = x, and the equation x = ± x becomes x = x. Dividing both sides of this equation by x yields 1 = 1. This is contradiction.
Hence, x cannot be positive. The answer is (D).
Answer: D
Question: Maddie has 24 apples, if she give 12 to mike, how many does she have left?
Options:
A)12
B)14
C)16
D)18
E)5
Rationale: 24-12=12
A 12
Answer: A
Question: A stick of 30 cm is broken into two pieces, what is the length of the shorter piece if the longer piece is 6 cm longer than the other?
Options:
A)11
B)10
C)12
D)13
E)7
Rationale: Since, 30 is the total length. Smaller is any one from answers.
Try Back solving from answer D, i.e. 12. 12+(12+6) = 31 > 30
Hence, Select next smaller no. : 12 +(12+6) =30.
So, 12 is the answer
Answer is C
Answer: C
Question: A shopkeeper sold an article for Rs 2552.36. Approximately what was his profit percent if the cost price of the article was Rs 2400
Options:
A)4%
B)5%
C)6%
D)7%
E)8%
Rationale: Explanation:
Gain % = (152.36*100/2400) = 6.34 % = 6% approx
Option C
Answer: C
Question: 2,5,10,17,?,41
Options:
A)26
B)27
C)29
D)25
E)28
Rationale: 2+3=5
5+5=10
10+7=17
17+11=28
28+13=41
ANSWER:E
Answer: E
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
Options:
A)5
B)6
C)7
D)9
E)2
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55 = 6 sec.
Answer: B
Answer: B
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 Nell bake?
Options:
A)0.125%
B)1.25%
C)12.5%
D)125%
E)0.152%
Rationale: 9.18x+5.17x+2.05x = 16.4x = 148 cookies
x= 148/16.4 = 9 (approx)
So, tell baked 9*2.05 cookies or 19 cookies (approx)
% share = 19/148 = 12.5 approx
Hence, answer is C.
Answer: C