divelab/Sys2Bench huggingface dataset:
Question: On the xy co-ordinate plane, point C is (5,-2) and point D is (-1,1.5). The point on line segment CD that is twice as far from C as from D is:
Options:
A)(1,-1)
B)(1,1)
C)(2,0.25)
D)(3,0.5)
E)(3,1)
Rationale: We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.
*It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:
Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)| = 6
The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is 5-4 = 1, or (-1)+2 = 1.
Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5| = 4.5
The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is (-2)+3 = 1, or 2.5-1.5 = 1.
So now we have our coordinates of the point on the line that is twice as far from C as it is from D: (3,1)
Answer: E
Answer: E
Question: In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been
Options:
A)24
B)144
C)326
D)292
E)584
Rationale: Explanation:
5 | x z = 13 x 1 + 12 = 25
--------------
9 | y - 4 y = 9 x z + 8 = 9 x 25 + 8 = 233
--------------
13| z - 8 x = 5 x y + 4 = 5 x 233 + 4 = 1169
--------------
| 1 -12
585) 1169 (1
585
---
584
---
Therefore, on dividing the number by 585, remainder = 584.
ANSWER 584
Answer: E
Question: The G.C.D. of 1.08, 0.36 and 0.9 is:
Options:
A)0.03
B)0.9
C)0.18
D)0.108
E)0.118
Rationale: Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18,
H.C.F. of given numbers = 0.18.
Answer: Option C
Answer: C
Question: If r and s are positive integers, and r^2 + r/s is an odd integer, which of the following cannot be even?
Options:
A)3r + 2s
B)(r-1)(s+2)
C)r^(s+1) + s^r
D)r^3 +3
E)s^4 +4
Rationale: Given: r and s are positive integers, and r2r2 + r/s is an odd integer
What are some "nice" values that make this true?
How about r = 2 and s = 2. We get: 2222 + 2/2 = 4 + 1 = 5, which IS an odd integer
Great, now let's plug r = 2 and s = 2 into each answer choice.
A. 3(2) + 2(2) = 10, which is even. so ELIMINATE A
B. (2 - 1)(2 + 2) = 4, which is even. so ELIMINATE B
C. 2^(2+1) + 2^2 = 12, which is even. so ELIMINATE C
D. 23+323+3 = 11, which is odd. so KEEP D for now
E. 24+424+4 = 20, which is even. so ELIMINATE E
By the process of elimination, the answer must be D
Answer: D
Question: 117 + 1.017 + 0.117 + 1.0017 = ?
Options:
A)109.3657
B)119.7563
C)119.1357
D)119.5637
E)119.6753
Rationale: 117
1.017
0.117
+ 1.0017
--------
119.1357
---------
Answer is C.
Answer: C
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for $75 less, he could have gained 25%. What is the cost price?
Options:
A)220
B)274
C)250
D)280
E)222
Rationale: C
250
$250
CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => $250
Answer: C
Question: A cement mixture is composed of 3 elements. By weight, 1/4 of the mixture is sand, 2/5 of the mixture is water, and the remaining 14 pounds of the mixture is gravel. What is the weight of the entire mixture in pounds?
Options:
A)9
B)14
C)28
D)40
E)60
Rationale: Let the total weight be x.
Sand content= (1/4)x
Water content= (2/5)x
Gravel=x-(1/4)x-(2/5)x=(7/20)x=14
x=40
Then answer will be D=40
Answer: D
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?
Options:
A)1000
B)1991
C)2888
D)1777
E)1555
Rationale: 1120 = P [1 + (5*12/5)/100]
P= 1000
Answer:A
Answer: A
Question: The areas of the two spheres are in the ratio 1: 4. The ratio of their volume is?
Options:
A)1 : 4
B)1 : 9
C)1 : 8
D)1 : 3
E)1 : 1
Rationale: 4πr12 : 4πr22 = 1 : 4
r1 : r2 = 1 : 2
4/3 πr13 : 4/3 πr23
r13 : r23 = 1 : 8
Answer: C
Answer: C
Question: A positive number x is multiplied by 10, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?
Options:
A) 9/4
B) 3/2
C) 4/3
D) 2/3
E) 10/3
Rationale: sq rt(10x/3) = x
=> 10x/3 = x^2
=> x = 10/3
Ans - E
Answer: E
Question: Cost is expressed by the formula tb^4. If b is doubled, the new cost R is what percent of the original cost?
Options:
A)R=200
B)R=600
C)R=800
D)R=1600
E)R=50
Rationale: Original Cost C1=t1*b1^4
New Cost C2= t2*b2^4....only b is doubled so t2=t1 and b2=2b1
C2=t2*(2b1)^4
=16(t1*b1^4)
=16C1
16 times C1=>1600% of C1
Ans D=1600
Answer: D
Question: In what ratio must a grocer mix two varieties of pulses costing Rs.15 and Rs.20 per kg respectively so as to get a mixture worth Rs.16.50 per Kg?
Options:
A)3 : 7
B)5 : 7
C)7 : 3
D)7 : 5
E)None
Rationale: Solution
Required ratio = 3.50 : 1.50 = 35 : 15 = 7 : 3.
Answer C
Answer: C
Question: Anup was asked to find the value of 7/12 of a sum of money R. Instead of multiplying the same by 7/12,he divided it by 7/12 and his answer exceeded the correct answer by 95. The correct answer is:
Options:
A) 48
B) 89
C) 84
D) 69
E) 49
Rationale: R=12/7*x-7/12*x=95 --> x=84 --> 7/12*x=49.
So if bythe correct answerquestion means 7/12 of the amount then the answer should be E.
Answer: E
Question: A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?
Options:
A)2 hours
B)7 hours
C)5 hours
D)9 hours
E)3 hours
Rationale: |-----------20--------------------|
50 40
D = 20
RS = 50 – 40 = 10
T = 20/10 = 2 hours
Answer: A
Answer: A
Question: A man walks at a rate of 10 mph. After every ten miles, he rests for 6 minutes. How much time does he take to walk 40 miles?
Options:
A) 258
B) 318
C) 322
D) 324
E) 330
Rationale: To cover 40 miles the man needs (time) = (distance)/(rate) = 40/10 = 4 hours = 240 minutes. He will also rest 3 times (after 10, 20, and 30 miles), so total resting time = 3*6 = 18 minutes.
Total time = 240 + 18 = 258 minutes.
Answer: A.
Answer: A
Question: What is the difference between the CI on Rs. 5000 for 1 years at 4% per annum CI yearly and half yearly?
Options:
A)Rs. 2.04
B)Rs. 3
C)Rs. 4.50
D)Rs. 5
E)Rs. 6.50
Rationale: C.I. when interest
compounded yearly
= Rs. 5000 x 1 + 4 x 1 + x 4
100 100
= Rs. 5000 x 26 x 51
25 50
= Rs. 5304.
C.I. when interest is
compounded half-yearly
= Rs. 5000 x 1 + 2 3
100
= Rs. 5000 x 51 x 51 x 51
50 50 50
= Rs. 5306.04
Difference = Rs. (5306.04 - 5304) = Rs. 2.04
A
Answer: A
Question: Of the female students at Barkely University, 1/6 are on the honor roll. Of the male students, 2/5 are on the honor roll. If 3/5 of the students are female, what is ratio of male to female students on honor roll?
Options:
A)8/5
B)3/15
C)23/30
D)43/60
E)53/90
Rationale: let the total students be 100
given 3/5 of the students are females = 60
then males = 2/5 = 40
1/6 of the females are on honor roll = 10
males on the honor roll = 2/5= 16
ratio of M:F students on honor roll = 16/10 = 8/5
A
Answer: A
Question: A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?
Options:
A)33 days
B)27 days
C)24 days
D)18 days
E)17 days
Rationale: 2c = 1/4 + 1/6 – 1/3 = 1/12
c = 1/24 => 24 days
Answer: C
Answer: C
Question: If 4 men can colour 48 m long cloth in 2 days, then 5 men can colour 36 m long cloth in
Options:
A)1.2 day
B)2.0 days
C)3 days
D)4.2 days
E)5 days
Rationale: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 5 = 1.2 day.
A
Answer: A
Question: If s=1 and (s-b)/c = 1 which of the following is NOT a possible value of b?
Options:
A)-2
B)-1
C)0
D)1
E)2
Rationale: Equation is:
(s-b)/c = 1 where s = 1
so plug in 1 for s and look at it again
(1-b)/c = 1
now C can be anything we want, so if b = -2 we can plug it in and make it work
(1-(-2))/c = 1
3/c = 1
c = 3 and it works
HOWEVER, if we have a 0 in the numerator there isn't a number on earth that makes 0/C = 1
(1-1)/c = 1
0/c = 1
there aren't any matches for C to make this true
B cannot be 1.
Answer is D
Answer: D
Question: A certain factory employed 600 men and 400 women and the average wager was Rs. 25.50 per day, If a woman got Rs. 5 less than a man, then what are their daily wages ?
Options:
A)m:25.50 w:27.50
B)m:27.50 w:22.50
C)m:26.50 w:27.50
D)m: 24.50 w:26.50
E)None of these
Rationale: Explanation:
Let the daily wage of a man be Rs. x.
Then, daily wage of a woman = Rs. (x - 5).
Now, 600x + 400 (x - 5) = 25.50 * (600 + 400) <=> 1000x = 27500 <=> x = 27.50.
Man's daily wages = Rs. 27.50; Woman's daily wages = (x - 5) = Rs. 22.50. Answer: B
Answer: B
Question: What is the sum of all remainders obtained when the first 100 natural numbers are divided by 7?
Options:
A)397
B)401
C)403
D)405
E)364
Rationale: A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0.
1 divided by 9 gives the remainder of 1;
2 divided by 9 gives the remainder of 2;
...
8 divided by 9 gives the remainder of 8;
9 divided by 9 gives the remainder of 0.
We'll have 11 such blocks, since 99/9=11. The last will be:
91 divided by 9 gives the remainder of 1;
92 divided by 9 gives the remainder of 2;
...
98 divided by 9 gives the remainder of 8;
99 divided by 9 gives the remainder of 0.
The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be:
11(1+2+3+4+5+6+7+8+0)+1=364.
Answer: E.
Answer: E
Question: If the equation x^2−6x=2k has at least one solution, which of the following must be true?
Options:
A)k > 9
B)k < −9
C)k = 9
D)k ≤ 9
E)k ≥ −9/2
Rationale: x^2−6x=2k
=> x^2−6x - 2k = 0
For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative.
b^2-4ac ≥0
=> 36 - 4*1*(-2k) ≥0
=> 36 + 8k ≥0
=> k ≥ -9/2
Answer E
Answer: E
Question: Find the greatest number which divides 83, 125 and 209 leaving the same remainder in each case.
Options:
A)19
B)17
C)42
D)23
E)32
Rationale: The greatest number which divides three dividends p, q and r leaving the same remainder in each case is given by H.C.F(any two of (q - p), (r - p) and (r - q)).
For the given problem, p = 83, q = 125 and r = 209.
Hence the greatest number which divides these three leaving the same remainder in each case is H.C.F(any two of (125 - 83, 209 - 83, 209 - 125) = 42.
ANSWER:C
Answer: C
Question: A student multiplied a number by 3/5 instead of 5/3. What is the percentage error.
Options:
A)64%
B)65%
C)66%
D)67%
E)68%
Rationale: Explanation:
Let the number be x,
then,
5/3−3/5=16/15x
Error% =
(16/15x∗3/5∗100)
Answer: Option A
Answer: A
Question: A and B both work for the same company. A goes to work Monday through Thursday, and B goes to work Tuesday thru Thursday. A takes 2 weeks of vacation per year, and B only takes 1 week. They do not take their vacations during the same week. What percent of the year can they carpool to work together, assuming they both have the same schedule? 1 year = 52 weeks = 364 days
Options:
A)42.9%
B)56.4%
C)45.6%
D)27.2%
E)40.4%
Rationale: A works M T W Th and B works T W Th
A and B work the same days on T W TH or 3/7
They don't work the same schedule for 3 weeks out of 52.
For 49 of the 52 weeks (i.e. 49/52=94.2%) they can carpool 3 days each week (i.e. 3/7=42.9%)
In a year, they can carpool 49/52 x 3/7 = 147/364 or 40.4% of the year.
Answer is E
Answer: E
Question: 9 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
Options:
A)12/9 days
B)15/2 days
C)82/8 days
D)22/76 days
E)22/2 days
Rationale: 9M = 6W ---- 20 days
12M + 8W -----?
8W + 8 W = 16W ---?
6W ---- 20 16 -----?
6 * 20 = 16 * x => x = 15/2 days
Answer:B
Answer: B
Question: The average of temperatures at noontime from Monday to Friday is 60; the lowest one is 50, what is the possible maximum range of the temperatures?
Options:
A)50
B)25
C)40
D)45
E)75
Rationale: Average=60, Sum of temperatures=60*5=300
As the min temperature is 50, max would be 300-4*50=100 --> The range=100(max)-50(min)=50
Answer: A
Answer: A
Question: Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected?
Options:
A)8/35
B)34/35
C)27/35
D)21/32
E)33/35
Rationale: Solution:
P(A) = 2/5
P(B) = 4/7
E = {A and B both get selected}
P(E) = P(A)*P(B)
= 2/5 * 4/7
= 8/35
ANSWER IS A
Answer: A
Question: A certain no. when divided by 50 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
Options:
A)2
B)4
C)5
D)8
E)9
Rationale: Explanation:
50 + 25 = 75/15 = 5 (Remainder)
C
Answer: C
Question: Pandiyan buys an old scooter for Rs. 6000 and spends Rs. 600 on its repairs. If he sells the scooter for Rs. 7200, his gain percent is :
Options:
A)20%
B)12%
C)9.09%
D)5%
E)None of these
Rationale: Explanation :
Solution: C.P. =Rs. (6000+600) =Rs. 6600; S.P. = Rs. 7200.
Gain% = 7200-6600/6600*100 = 9.09%
Answer : C
Answer: C
Question: 500 x (200 + 4) Ã— (3 + 2) = ?
Options:
A)55000
B)450000
C)250000
D)410000
E)510000
Rationale: 500 x204 x 5 =510000 Answer : E
Answer: E
Question: Two tains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
Options:
A)12
B)24
C)36
D)48
E)38
Rationale: Sol.
Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 ⇔ 2x = 20 ⇔ x = 10.
∴ Speed of each train = 10 m/sec = [10 * 18/5] km/hr = 36 km/hr.
Answer C
Answer: C
Question: If a certain sample of data has a mean of 25.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
Options:
A)12.0
B)13.5
C)17.0
D)23.5
E)26.5
Rationale: Value ismore than 2.5SDfrom the mean means that the distance between the mean and the value must be more than 2.5*SD=7.5. So the value must be either less than 25-7.5=17.5.5or more than 25+7.5=32.5.
Answer: C.
Answer: C
Question: The number 0.650 is how much greater than 1/8 ?
Options:
A)½
B)21/40
C)1/50
D)1/500
E)2/500
Rationale: let x be the difference
then
.65-1/8=x
65/100-1/8=x
x=21/40
ans B
Answer: B
Question: Which of the following multipliers will cause a number to be increased by 29.7%?
Options:
A)1.297
B)12.97
C)129.7
D)1297
E)None
Rationale: Solution
Let the number be 100 and required multiplier be y.
Then, 100y = 129.7
y = 129.7 / 100
= 1.297
Answer D
Answer: D
Question: How many diagonals does a polygon with 17 sides have, if one of its vertices does not connect to any diagonal?
Options:
A)102
B)104
C)110
D)90
E)84
Rationale: If I calculate it using the formulae, #diagonals = n (n-3)/2Each vertex sends of n-3 diagonals
n= 17-1 then 16*(16-3)/2 = 104
Correct Option:	B
Answer: B
Question: For any real number x, the operatoris defined as:
(x) = x(6 − x)
If p + 1 =(p + 1), then p =
Options:
A)−2
B)0
C)1
D)2
E)5
Rationale: (x) = x(6 − x)
(p + 1) = (p + 1)(6 - p - 1) = (5-p)(p+1)
We are given that p + 1 =(p + 1)
Therefore (5-p)(p+1) = (p + 1)
Or (p + 1) + (5-p)(p+1) = 0
(p + 1)(p-5) = 0
p = -1,p=5
Option E
Answer: E
Question: Diane find 6 cans of paint are just enough to paint one third of her room. How many more cans of paint will she need to finish her room and paint a second room of the same size?
Options:
A)5
B)7 and a half
C)10
D)12 and a half
E)30
Rationale: She will need 12 cans to paint the rest of this room and 18 for the next room for a total of 30 cans.
E
Answer: E
Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 15 minutes. How long will it take to go 5 km in stationary water?
Options:
A)40 minutes
B)1 hour
C)1 hour 15 min
D)1 hour 30 min
E)1 hour 40 min
Rationale: speed (upstream) =2/1 = 2 kmhr
speed (downstream)=1/(15/60)= 4 kmhr
speed in still water = 1/2 (2+4) = 3 kmhr
time taken in stationary = 5/3 = 1 hrs 40 min
ANSWER:E
Answer: E
Question: The average wages of a worker during a fortnight comprising 15 consecutive working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $91 per day. What was his wage on the 8th day?
Options:
A)$83
B)$90
C)$92
D)$97
E)$104
Rationale: Average daily wage of a worker for 15 consecutive working days = 90$
During the first 7 days , the daily average daily wage = 87$
During the last 7 days , the daily average daily wage = 91$
Wage on 8th day = 90*15 -( 87*7 + 91 *7)
= 1350 - (609 + 637)
=1350 - 1246
= 104
Answer E
Answer: E
Question: If two numbers are in the ratio 2:3. If 5 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
Options:
A)A)10
B)B)20
C)C)25
D)D)30
E)E)35
Rationale: 2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 5] = 3[3x + 5]
8x + 20 = 9x + 15
9x - 8x = 20 - 15
x = 5
Then smallest number is = 2
2x = 10
Correct Option A
Answer: A
Question: A thief is spotted by a policeman from a distance of 300metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 16km/hr and that of the policeman 20km/hr, how far the thief will have run before he is overtaken ?
Options:
A)A)1km
B)B)500m
C)C)650m
D)D)750m
E)E)1200m
Rationale: Relative speed of the policeman = 20-16 = 4 km/hr
time taken by policeman to cover 300m = (300/1000)*(1/4) = 3/40 hr
In 3/40 hr the thief covers a distance of 48/40 km = 6/5 km = 1200m
Answer is E
Answer: E
Question: √(14)^2
Options:
A)7
B)14
C)49
D)21
E)None of these
Rationale: explanation
√(14)^2 =?
or, ? = 14
Answer B
Answer: B
Question: 12 men work 8 hours per day to complete the work in 10 days. To complete the same work in 8 days, working 15 hours a day, the number of men required?
Options:
A)8 days
B)9 days
C)11 days
D)13 days
E)15 days
Rationale: That is, 1 work done = 12 × 8 × 10
Then, 12 8 × 10 = ? × 15 × 8
? (i.e. No. of men required) = 12 × 8 × 10/15× 10 = 8 days.
A)
Answer: A
Question: The sale price sarees listed for Rs.400 after successive discount is 15% and 5% is?
Options:
A)297
B)879
C)323
D)762
E)269
Rationale: 400*(85/100)*(95/100)
= 323
Answer: C
Answer: C
Question: Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 9180, how much money did he borrow?
Options:
A)9000
B)80288
C)2668
D)2600
E)2781
Rationale: Let the sum be Rs. x. Then,
[(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 9180
18x + 45x + 39x = (9180 * 100)
102x = 918000 => x = 9000.
Answer:A
Answer: A
Question: If a trader sold two cars each at Rs. 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?
Options:
A)1.44
B)1.42
C)1.49
D)1.42
E)1.43
Rationale: SP of each car is Rs. 325475, he gains 12% on first car and losses 12% on second car.
In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (12)(12)/100 % = 1.44%
Answer:A
Answer: A
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 2 years hence?
Options:
A)58
B)59
C)64
D)70
E)74
Rationale: Explanation:
A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
2 years, their ages will be 42 and 22.
Sum of their ages = 42 + 22 = 64.
C)
Answer: C
Question: A, B and C can do a work in 6, 9 and 12 days respectively doing the work together and get a payment of Rs.1800. What is B’s share?
Options:
A)Rs.245.8
B)Rs.653.8
C)Rs.300
D)Rs.400
E)Rs.748.5
Rationale: WC = 1/6:1/9:1/12 => 6:4:3
4/13 * 1800 = 653.8
ANSWER:B
Answer: B
Question: A large kennel has a gate for dogs to enter and a gate for dogs to exit. The kennel can be filled with dogs who use the entrance in 5 hours. The exit gate can be used to empty the kennel in 15 hours. If it is desired that the kennel should be filled, from empty, exactly 6 hours after the entrance gate is opened at 9:30am, then at what time should the exit gate be opened ?
Options:
A)10:00am
B)10:45am
C)12:00pm
D)12:30pm
E)1:30pm
Rationale: In 6 hours the entrance gate can accept the amount of dogs equal to 6*1/5 = 6/5 of the kennel. So, 1/5 more than necessary, which should be compensated by the exit gate. To ride the kennel 1/5 of the dogs the exit gate needs 15/5 = 3 hours.
Therefore, the exit gate should be opened at 9:30am + 6 hours - 3 hours = 12:30pm.
Answer: D.
Answer: D
Question: At Veridux Corporation, there are 250 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. If there are a total of 155 male associates, how many female managers are there?
Options:
A)15
B)20
C)25
D)30
E)35
Rationale: 250 Employees:
90 Male, 160 Female
40 Managers, 210 Associates
155 Male Associates implies 55 Female Associates which means the remaining 35 females must be Managers
E. 35
Answer: E
Question: On a trip, a cyclist averaged 8 miles per hour for the first 16 miles and 10 miles per hour for the remaining 16 miles. If the cyclist returned immediately via the same route and took a total of 6.8 hours for the round trip, what was the average speed (in miles per hour) for the return trip?
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: The time to go 32 miles was 16/8+16/10=2+1.6=3.6 hours.
The average speed for the return trip was 32 miles/3.2 hours= 10 mph.
The answer is B.
Answer: B
Question: What is the minimum value of z for which z^2 + z - 3/14 > 0 is not true?
Options:
A) -5/7
B) -3/7
C) -1/7
D) 1/7
E) 4/7
Rationale: I think B -3/7 is the best ans...
Answer: B
Question: Goldenrod and No Hope are in a horse race with 7 contestants. How many different arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?
Options:
A)5040
B)2520
C)1200
D)240
E)210
Rationale: All 7 horses can finish the race in 7! way (assuming no tie).
If no tie is possible between No Hope and Goldenrod, then in half of these cases No Hope will be before Goldenrod and in half of these cases after (not necessarily right before or right after). How else? So, there are 7!/2=2520 different arrangements of finishes where No Hope always finishes before Goldenrod.
Answer: B.
Answer: B
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
Options:
A)3 1/5 Km
B)2 1/5 Km
C)4 1/5 Km
D)5 1/5 Km
E)6 1/5 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 16/6
= 24/2 * 16/60
= 8 * 2/5
= 16/5 = 3 1/5 Km
Answer: Option 'A'
Answer: A
Question: As a bicycle salesperson, David earns a fixed salary of $25 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true? I. y<3x II. y>x III. y>1
Options:
A)I,III only
B)III only
C)I only
D)II only
E)II,III only
Rationale: II. y>x --> since this week, David earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week);
III. y>1 --> if David sold 3 bicycles this week then this week he earned 25+3*6=$43, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $25. So y must be more than 1;
I. y<3x --> is not always true.
Answer: E
Answer: E