divelab/Sys2Bench huggingface dataset:
Question: If the speed of X meters per second is equivalent to the speed of Y meters per hour, what is Y in terms of X? (1 kilometer=1000 meters)
Options:
A)15x/18
B)6x/5
C)18x/5
D)60x
E)3600x
Rationale: If the speed of X meters per second is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)
We need to find an equation with x in the answer...
convert all measurements so they are alike (i.e. convert km to m, seconds to hours, etc)
Speed = x/t
x meters/second
(3600) x meters/hour
Speed = y/t
y M/hour
Speed = y/hour
y/hour = (3600) x meters/hour
y/1hour = x(3600) / 1 hour
y= x(3600)
y = 3600x
Answer: E.
Answer: E
Question: if 11 oranges bought 10 r and 10 oranges sold 11 r .what is the profit
Options:
A)11 %
B)20 %
C)22 %
D)21 %
E)23 %
Rationale: suppose he bought 110 apples.
cp= Rs 100
SP=Rs 121
% profit = 100*(121-100)/100 = 21 %
ANSWER:D
Answer: D
Question: What is the maximum number of slices can you obtain by cutting a cake with only 4 cuts?
Options:
A)9
B)12
C)14
D)16
E)18
Rationale: step 1: cut the cake from middle in two equal pieces. this is the first cut and we get two pieces.
step 2: put one piece on the other piece vertically and cut them from top to bottom. this is the 2nd cut and we have 4 piece.
step 3: again put the 4 pieces on each other vertically and cut from top to bottom. this is 3rd cut and we have 8 piece.
step[ 4: again put all the 8 pieces on each other vertically and cut from top to bottom. this is the 4th cut and we have 16 equal piece.
ANSWER:D
Answer: D
Question: Raman covers 1 km in 8 min while suman covers the same distance in 10 min. By what distance does Raman beat Suman ?
Options:
A)150 m
B)65 m
C)190 m
D)200 m
E)220 m
Rationale: Raman covers 1 km in 8 min
and suman cover 1 km in 10 min.
If they starts together, then distance covered by suman in 8 min
= (1000/10) x 8 = 800 m
∴ Raman will beat suman by (1000 - 800 ) m = 200 m
ANSWER :D
Answer: D
Question: How much 60% of 50 is greater than 40% of 30?
Options:
A)18
B)28
C)26
D)27
E)23
Rationale: (60/100) * 50 – (40/100) * 30
30 - 12 = 18
Answer:A
Answer: A
Question: If 16 machine can finish a job in 45 days, then how many more machines would be needed to finish the job in one -third less time?
Options:
A)a. 3
B)b. 8
C)c. 10
D)d. 12
E)e. 16
Rationale: You might think of this in a management context - we can use the principle of 'person-hours' to solve any problem where we have identical workers. So, using simpler numbers, suppose you know that 6 identical employees, working simultaneously, would finish a job in 5 hours. Then that job requires 6*5 = 30 total hours of person-work. If instead you wanted the job done in 3 hours, you'd assign 30/3 = 10 employees to do the job, because you want to get a total of 30 hours of work from the employees.
We can solve this problem identically. If 16 machines (identical ones, I assume) work simultaneously for 45 days, they will do a total of 16*45 machine-days of work. So the job requires 16*45 days of machine work in total. We instead want the job done in 1/3 less time, so in 30 days. So we'll need 16*36/30 = 19.2 ~=19 machines, or 3 additional machines.
A
Answer: A
Question: A cubical rectangular bar has the dimensions with the ratio 5 : 4 : 3. Its volume is 7500. What
is the surface area of the bar?
Options:
A)1350
B)2350
C)4350
D)5640
E)8456
Rationale: volume of cubiod is lbh:5x*4x*3x=7500;
x=5
now,area is 2(lb+bh+lh):2(25*20+20*15+25*15)=2350.
therefore,area=2350
ANSWER:A
Answer: A
Question: In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 7 : 32. In the company, what is the maximum number of non-managers in a department that has 8 managers?
Options:
A)35
B)36
C)37
D)38
E)39
Rationale: 8/7 * 32 = 36.6
The answer is B.
Answer: B
Question: 1/2 + [(2/3 * 3/8)*4] - 9/16 =
Options:
A) 29/16
B) 19/16
C) 15/16
D) 9/13
E) 0
Rationale: We need to simplify the expression using PEMDAS.
Parentheses
Exponents
Multiplication andDivision
Addition andSubtraction
The calculation of an equation or expression must be carried out in the following order:
1) Operations within parentheses (or absolute value bars or radicals)
2) Exponents
3) Multiplication and division from left to right
4) Addition and subtraction from left to right
The answer is C.
Answer: C
Question: If a positive odd integer N has p positive factors, how many positive factors will 2N have ?
Options:
A)p
B)2p
C)P+1
D)2p+1
E)Cannot be determined
Rationale: no of factor of a=b^m * c^n * d^o * e^q.... = (m+1)*(n+1)*(o+1)*(q+1)...
Given that N is an odd integer. So N can be b^m * c^n * d^o * e^q, where b,c,d,e are odd numbers.
The number of factors of N = (m+1)*(n+1)*(o+1)*(q+1) = p
For a number 2N = 2^1 * b^m * c^n * d^o * e^p, number of factors will be (1+1)*(m+1)*(n+1)*(o+1)*(q+1) = 2*p
So, number of factors of 2N = 2*p
Hence, answer will be B.
Answer: B
Question: What is the remainder when 1234 * 6789 * 1111 is divided by 19
Options:
A)15
B)23
C)7
D)10
E)43
Rationale: 12345/19==> Remainder=14
678910/19==> Remainder=2
111111/19==> Remainder=18
=14*2*18=504/19==> Remainder=10
Answer: D
Answer: D
Question: Aaron will jog from home at 3 miles per hour and then walk back home by the same route at 6 miles per hour. How many miles from home can Aaron jog so that he spends a total of 3 hours jogging and walking?
Options:
A)3
B)6
C)2
D)5
E)8
Rationale: xyt/(x+y)
x= 3, y=6, t= 3
3*6*3/3+6 = 54/9 = 6
Answer : B
Answer: B
Question: Integer x is equal to the product of all even numbers from 2 to 60, inclusive. If C is the smallest prime number that is also a factor of x-1, then which of the following expressions must be true?
Options:
A) 0<y<4
B) 4<y<10
C) 10<y<20
D) 20<y<30
E) y>30
Rationale: C Smallest prime factor is greater than 29. So answer is E
Answer: E
Question: The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10 n, on the nth day of 2007 (n = 1, 2, ..., 100), and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15n, on the nth day of 2007 (n = 1, 2, ..., 365). On which date in 2007 will the prices of these two varieties of tea be equal ?
Options:
A)May 21
B)April 11
C)May 20
D)April 10
E)June 30
Rationale: Explanation :
Price of Darjeeling tea (in rupees per kilo gram) is 100 + 0.10n
Price of Ooty tea (in rupees per kilo gram) is 89 + 0.15n
Price of the Darjeeling tea on the 100th day = 100 + 0.1 × 100 = 110.
=> 89 + 0.15n = 110.
=> n = 140.
Number of days in the months of January, February, March and April in the year 2007 = 31 + 28 + 31 + 30 = 120.
Therefore, the price of both the tea will be equal on 20th May.
Answer : C
Answer: C
Question: Average monthly income of a family of 4 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 650. The income of the deceased was?
Options:
A)Rs. 692.80
B)Rs. 820
C)Rs. 990
D)Rs. 1385
E)None
Rationale: Answer
Income of the deceased = Total income of 4 members - total income of remaining 3 members.
= 735 x 4 - 650 x 3 Rs.
= 990 Rs.
Correct Option: C
Answer: C
Question: he time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
Options:
A)12 kmph.
B)17 kmph.
C)14 kmph.
D)21 kmph.
E)19 kmph.
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 42/3 = 14 kmph.
Answer: C
Answer: C
Question: A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?
Options:
A)39:40
B)39:47
C)39:50
D)39:44
E)39:41
Rationale: 3: 4
A = 3/7*210 = 90
390: 400
39:40.Answer:A
Answer: A
Question: What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
Options:
A)20(2/3)%
B)20%
C)21%
D)22(2/3)%
E)None of these
Rationale: Explanation :
Total numbers = 70
Total numbers in 1 to 70 which has 1 in the unit digit = 7
Total numbers in 1 to 70 which has 9 in the unit digit = 7
Total numbers in 1 to 70 which has 1 or 9 in the unit digit = 7 + 7 = 14
Required percentage = (14/70) × 100 = 140/7 = 20%
Answer : Option B
Answer: B
Question: If 2x + 3y = 70; 2y + z = 19 and x + 2z = 29, what is the value of x + y + z ?
Options:
A)18
B)32
C)36
D)22
E)None of these
Rationale: On solving equation we get
x = 27, y = 8, z = 1
Answer C
Answer: C
Question: Two trains of length 160 m and 320 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
Options:
A)10 sec
B)32 sec
C)82 sec
D)24 sec
E)89 sec
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 160 + 320 = 480 m.
The time required = d/s = 480 /20 = 24 sec.
Answer:D
Answer: D
Question: Which is a tool that helps RBI to stabilize money supply and prices of Government securities?
Options:
A)OMJ
B)OMY
C)OMO
D)OM6
E)OMD
Rationale: Explanation:
An Open Market Operation is an activity by a central bank to buy or sell government bonds on the open market.
ANSWER: C
Answer: C
Question: A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 140, how many coins of each type are there?
Options:
A)20 coins
B)30 coins
C)40 coins
D)80 coins
E)None of these
Rationale: Let number of each type of coin = x. Then,
1 × x + .50 × x + .25x = 140
⇒ 1.75x = 140 ⇒ x = 80 coins
Answer D
Answer: D
Question: Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
Options:
A)11
B)10
C)817
D)117
E)111
Rationale: Explanation:
Part of the filled by all the three pipes in one minute
= 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10
So, the tank becomes full in 10 minutes.
Answer:D
Answer: D
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.200 in 4 Years?
Options:
A)5%
B)7%
C)6.25%
D)2%
E)4%
Rationale: 200 = (800*4*R)/100
R = 6.25%
Answer: C
Answer: C
Question: Jane spent $42 for shoes. This was $14 less than twice what she spent for a blouse. How much was the blouse?
Options:
A)32
B)28
C)17
D)45
E)63
Rationale: Let x, then, be how much she spent for the blouse. The problem states that "This" -- that is, $42 -- was $14 less than two times x.
Here is the equation:
2x − 14 = 42.
2x = 42 + 14
= 56.
x = 56
/2
= 28.
The blouse cost $28.
Answer: B
Question: Sri travels the first 6 hours of his journey at 40 mph speed and the remaining 3 hours at 20mph speed. What is the average speed of Sri's travel in mph?
Options:
A)33.3mph
B)33.8mph
C)32.3mph
D)34.3mph
E)33.1mph
Rationale: Explanation :
Average speed=Total Distance/Time.
Total distance travelled by sri = Distance covered in the first 6 hours + Distance covered in the next 3 hours.
Distance covered in the first 6 hours = 6Ã—40=240 miles
Distance covered in the next 3 hours= 3Ã—20=60 miles
Therefore, total distance travelled = 240+60=300 miles.
The total time taken = 6+3=9hours.
Hence, the average speed =300/9= 33.3mph.
Answer : A
Answer: A
Question: How much time will take for an amount of Rs. 300 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
Options:
A)7
B)4
C)6
D)3
E)2
Rationale: Time = (100 * 81) / (300 * 4.5) = 6 years'
Answer:C
Answer: C
Question: A rope of which a calf is tied is increased from 15 m to 18m, how much additional grassy ground shall it graze?
Options:
A)1218
B)1212
C)1210
D)3.11.14
E)291.1
Rationale: π (182 – 152) = 311.14
Answer: D
Answer: D
Question: At the time of marriage, a man was 6 years elder to his wife. 6 years after their marriage, his age is 8/7 times the age of his wife. What was wife's age at the time of marriage ? Choose one answer.
Options:
A)25 years
B)30 years
C)18 years
D)24 years
E)36 years
Rationale: let wifes age= x
husband age = x+6
now after 6 years of mrg x+6 wifes age
x+6+6 husbands age
8/7(x+6)=x+6+6
after solving x=36
ANSWER:E
Answer: E
Question: In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 60 per square m?
Options:
A)Rs. 50000
B)Rs. 52000
C)Rs. 57000
D)Rs. 60000
E)Rs. 61000
Rationale: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m
Total area of the hall to be covered with mat = 2(lb + bh + hl)
= 2(20 * 15 + 15 * 5 + 5 * 20)
=2(300 + 75 + 100)
= 2 * 475
= 950 sq. m
Total expenditure = 60 * 950
= Rs. 57000
C
Answer: C
Question: A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
Options:
A)75%
B)50%
C)100%
D)80%
E)70%
Rationale: MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
ANSWER:C
Answer: C
Question: Two employees A and B are paid a total of Rs. 580 per week by their employer. If A is paid 150 percent of the sum paid to B, how much is B paid per week?
Options:
A)s.130
B)s.140
C)s.150
D)s.232
E)s.280
Rationale: Let the amount paid to A per week = x
and the amount paid to B per week = y
Then x + y = 580
But x = 150% of y = 150y/100 = 15y/10
∴15y/10 + y = 580
⇒ y[15/10 + 1] = 580
⇒ 25y/10 = 580
⇒ 25y = 5800
⇒ y = 5800/25 = Rs.232
D)
Answer: D
Question: The train travels at an average speed of 25km/h, to the top of the hill where the midpoint of the trip is. Going down hill, train travels at an average speed of 5km/h. Which of the following is the closest approximation of train's average speed, in kilometers per hour, for the round trip?
Options:
A)8.5
B)8.3
C)2.6
D)4.2
E)6.5
Rationale: Since we're not given a distance to work with, we can TEST any distance that we like. Here, since the speeds are 25 km/hour and 5 km/hour, using a multiple of both 25 and 5 would make the math easiest.
Let's set the Distance up the hill at 50 km.
So, going uphill, we have....
D = (R)(T)
50 = (25)(T)
50/25 = 2 = T
2 hours to go uphill
Going downhill, we have....
D = (R)(T)
50 = (5)(T)
50/5 = 10 = T
10 hours to go downhill
Total Distance = 100 km
Total Time = 10+2 = 12 hours
Average Speed = 100/12 = 8.3 km/hour
B
Answer: B
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 27.3%. What would have been the percentage of profit earned if no discount had been offered?
Options:
A)28.5
B)27.675
C)30
D)34%
E)None of these
Rationale: Giving no discount to customer implies selling the product on printed price. Suppose the cost price of the article is 100.
Then printed price = 100Ã—(100+27.3)/(100âˆ’5)
= 100Ã—127.3/95=134
Hence, required % Profit = 134 â€“ 100 = 34%
Answer D
Answer: D
Question: A pharmaceutical company received $6 million in royalties on the first $20 million in sales of the generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?
Options:
A)8%
B)15%
C)45%
D)52%
E)72%
Rationale: Solution:
This is a percent decrease problem. We will use the formula: percent change = (new – old)/old x 100 to calculate the final answer.
We first set up the ratios of royalties to sales. The first ratio will be for the first 20 million in sales, and the second ratio will be for the next 108 million in sales. Because all of the sales are in millions, we do not have to express all the trailing zeros in our ratios.
First 20 Million
royalties/sales = 6/20 =3/10
Next 108 Million
royalties/sales = 9/108 = 1/12
Because each ratio is not an easy number to use, we can simplify each one by multiplying each by the LCM of the two denominators, which is 60. Keep in mind that we are able to do this only because our answer choices are expressed in percents.
First 20 Million
royalties/sales = (6/20) x 60 = 18
Next 108 Million
royalties/sales = 9/108 = (1/12) x 60 = 5
We can plug 18 and 5 into our percent change formula:
(new – old)/old x 100
[(5 – 18)/18] x 100
-650/9 x 100
At this point we can stop and consider the answer choices. Since we know that 650/9 is just a bit less than ½, we know that -650/9 x 100 is about a 72% decrease.
Answer E.
Answer: E
Question: X and Y walk around a circular track. They start at 10 a.m from the same point in the opposite directions. X and Y walk at a speed of 6 rounds per hour and 7 rounds per hour respectively. How many times shall they cross each other before 3 p.m
Options:
A)64
B)65
C)66
D)67
E)68
Rationale: Explanation:
Relative speed = (6+7) =13 rounds per hour
So, they cross each other 13 times in an hour hence, they cross 65 times before 3 p.m
Answer: Option B
Answer: B
Question: Sahil purchased a machine at Rs 14000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it.
Options:
A)Rs. 22000
B)Rs. 24000
C)Rs. 26000
D)Rs. 30000
E)None of these
Rationale: Explanation:
Question seems a bit tricky, but it is very simple.
Just calculate all Cost price, then get 150% of CP.
C.P. = 14000 + 5000 + 1000 = 20000
150% of 20000 = 150/100 * 20000 = 30000
Option D
Answer: D
Question: John's marks wrongly entered as 82 instead of 62. Due to that the average marks for the class got increased by half (1/2). The number of John in the class is?
Options:
A)70
B)78
C)80
D)84
E)90
Rationale: otal increase in marks = x x	1 =	x
2	2
x/2	= (82 - 62) x/2	= 40 x= 80.
C
Answer: C
Question: Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:
Options:
A)14
B)12
C)15
D)16
E)20
Rationale: Filled in 2 hrs = 2/6 = 1/3
remain = (1-1/3)=2/3
(A+B)'S 7 HRS WORK = 2/3
(A+B)'S 1 hr work = 2/21
C'S 1 hr work = (A+B+C)'S 1 hr work - (A+B)'S 1 hr work
=(1/6-2/21)=1/14
=>c alone fill tank in 14 hrs
ANSWER A
Answer: A
Question: The present worth of Rs.169 due in 2 years at 4% per annum compound interest is
Options:
A)Rs.150.50
B)Rs.154.75
C)Rs.156.25
D)Rs.158
E)None
Rationale: Solution
Present Worth	= Rs.[169/(1+4/100)²]
= Rs.(169x25/26x25/26)
= Rs.156.25
Answer C
Answer: C
Question: A tailor trims 6 feet from opposite edges of a square piece of cloth, and 5 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?
Options:
A)20
B)22
C)24
D)26
E)28
Rationale: Let the original side of the square be x.
(x-12)*(x-10) = 120 = 10*12
x = 22
The answer is B.
Answer: B
Question: If a*b=2a-3b+ab,then3*5+5*3 is equal to
Options:
A)22
B)32
C)25
D)28
E)30
Rationale: 3*5+5*3= (2x3-3x5+3x5)+(2x5-3x3+5x3)
=22
ANSWER A 22
Answer: A
Question: A, B and C can do a piece of work in 5 days, 10 days and 15 days respectively. How long will they taken, if all the three work together?
Options:
A)2
B)4
C)2 8/11
D)67
E)9
Rationale: 1/5 + 1/10 + 1/15 = 11/30 => 30/11 => 2 8/11 days
Answer: C
Answer: C
Question: A chair is bought for Rs.900/- and sold at Rs.810/- find the loss percentage
Options:
A)10% Gain
B)10% Loss
C)20% Loss
D)25% Loss
E)30% Loss
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (810 ~ 900)/900 = 10% Loss
B
Answer: B
Question: If 9!/3^x is an integer, what is the greatest possible value of x?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 9 - 3*3
6 - 2*3
3 - 1*3
Hence max of 3^4 is allowed. IMO B.
Answer: B
Question: eight children, Arya, Betsy, Chen, Daniel, Emily, and Franco, are to be seated in a single row of six chairs. If Betsy cannot sit next to Emily, how many different arrangements of the six children are possible?
Options:
A)240
B)480
C)540
D)720
E)840
Rationale: Since it is more time consuming and error prone to find ways Betsy and E not sitting together, It is better we find ways in which they will be together and then subtract from total ways..
total ways = 6!..
ways B and E will be sitting together..
take both B and E as one, then these two together with other 4 can sit in 5! ways ...
Also B and E can sit within themselves in 2! ways..
so the answer required = 6!-2*5!=720..
ans D
Answer: D
Question: Mr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 3 children and 6 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive?
Options:
A)16.25%
B)8.25%
C)4.25%
D)6.25%
E)7.25%
Rationale: 25/4 =6.25
Answer : D
Answer: D
Question: Egg Street begins at Toast Street and runs directly east for 6.6 kilometers until it ends when it meets Jam Street. Egg Street is intersected every 120 meters by a perpendicular street, and each of those streets other than Toast Street and Jam Street is given a number beginning at 1st Street (one block east of Toast Street) and continuing consecutively (2nd Street, 3rd Street, etc...) until the highest-numbered street one block west of Jam Street. What is the highest-numbered street that intersects Egg Street?
Options:
A)52nd
B)53rd
C)54th
D)56th
E)57th
Rationale: 6.6 km / 120 m = 55.
However, the street at the 6.6-km mark is not 55th Street; it is Jam Street.
Therefore, the highest numbered street is 54th Street.
The answer is C.
Answer: C
Question: On flipping 3 coins together what is the outcomes for at least three tails?
Options:
A){HHH, HHT, HTH, THH}
B){HHT, HHT, HTH, THH}
C){TTH, HHT, HTH, THH}
D){TTT, HHT, HTH, THH}
E)None
Rationale: Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Favorable outcomes for at least three tails.
= favorable outcomes for exactlythree tails
= {TTT}
E
Answer: E
Question: If x and y are positive integers such that x < y and z=x/y, which of the following must be true?
I. z>(x − 1)/(y − 1)
II. z>(x − 1)/(y − 1)
III. z>(x + 1)/(y - 1)
Options:
A)II only
B)I and II
C)II and III
D)I only
E)I and III
Rationale: x < y --> Let x = 2 and y = 3 --> z = 2/3
I. z>(x − 1)/(y − 1) --> 2/3 > 1/2 --> True
II. z>(x − 1)/(y − 1) --> 2/3 > 1/2 --> True
III. z>(x + 1)/(y - 1) --> 2/3 > 3/2 --> False
Answer: B
Answer: B
Question: In a series of six consecutive even numbers, the sum of the fifth and sixth numbers is 42. What is the second number?
Options:
A)10
B)12
C)14
D)18
E)16
Rationale: Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10.
Given (x + 8) + (x + 10) = 42
=> 2x + 18 = 24 => x = 12
The second number = x + 2 = 12 + 2 = 14.
Answer: C
Answer: C
Question: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:
Options:
A)20
B)30
C)40
D)None of these
E)Either (a) or (b)
Rationale: Let the numbers be a, b and c.
Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400.
(a + b + c) = 400 = 20.
ANSWER : A
Answer: A
Question: P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
Options:
A)17:1
B)17:6
C)17:9
D)17:2
E)17:3
Rationale: P:Q = 85000 : 15000
= 17:3.
Answer:E
Answer: E
Question: Which of the following is not an odd function?
Options:
A)f(x) = -x3
B)f(x) = x5
C)f(x) = x2 - x
D)f(x) = |x|3
E)None of these
Rationale: Solution:
An odd function is a function whose value reverses in sign for a reversal in sign of its argument. i.e. f(x) = -f(-x).
Except f(x) = |x|3 all other functions mentioned in the choices change values.
Answer D
Answer: D