divelab/Sys2Bench huggingface dataset:
Question: If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster, he would have covered 70 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day?
Options:
A)100
B)120
C)140
D)150 miles
E)160
Rationale: Let v and t be initial parameter
vt=d
from the stem (t+1)(v+5)=70+d
=>v+5t=65-------1)
We need the additional distance traveled second time at v+10 and t+2
(t+2)(v+10)=vt+2v+10t+20
but vt=d
Hence d+2(v+5t)+20
But v+5t=65 hence the additional distance traveled is 2(v+5t)+20=2*65+20=130+20=150 D
Answer: D
Question: Using all the letters of the word "MONDAY", how many different words can be formed?
Options:
A)A)7
B)B)8!
C)C)8
D)D)6!
E)E)3
Rationale: Explanation:
Total number of letters = 6
Using these letters the number of 6 letters words formed is 6!.
Answer: Option D
Answer: D
Question: Five consecutive traffic signals each show either red or green. How many different arrangements of the five signals are possible?
Options:
A)40
B)32
C)28
D)17
E)6
Rationale: Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly.
We're told that 5 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 5 signals are possible.
Total Options: 32
Final Answer:
B
Answer: B
Question: A student has to obtain 60% of the total marks to pass. He got 160 marks and failed by 20 marks. The maximum marks are?
Options:
A)210
B)280
C)300
D)320
E)340
Rationale: Let the maximum marks be x
Then, 60% of x = 160+20
60x/100 = 180
60x= 180*100= 18000
x = 300
Answer is C
Answer: C
Question: By selling an umbrella for Rs. 600, a shop keeper gains 700%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?
Options:
A)733.33
B)833.33
C)933.33
D)533.33
E)433.33
Rationale: Marked price = Rs. 600
C.P. = 100/800 * 600 = Rs. 75
Sale price = 90% of Rs. 600 = Rs. 540
Required gain % = 700/75 * 100 = 933.33%.
Answer:C
Answer: C
Question: The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,6), (8,0) and (8,6). If a line through (2,2) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
Options:
A)0
B)2/5
C)4/7
D)1/2
E)7/4
Rationale: CONCEPT: The readers need to know that a rectangle can be divided into two equal area by a Straight line only when the straight line passes through the Centre of the Rectangle (Intersection of its two diagonals)Draw a figure and know it for yourself.
The point of Intersections of the diagonals will be the midpoint of any diagonal i.e. Midpoint of (0,0), and (8,6) OR Midpoint of (0,6) and (8,0)
i.e. Either [(0+8)/2, (0+6)/2] OR [(0+8)/2, (6+0)/2] =[4,3]
Slope of line passing through points (2,2) and (4,3) = (3-2)/(4-2) = 1/2
D
Answer: D
Question: An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 5 businessmen, how many possible team submissions are possible?
Options:
A)74
B)100
C)162
D)198
E)202
Rationale: We have 3 scenarios here:
1) 1 tech2 businessmen: 4C1 x 5C2 = 40
2) 2 tech1 businessman: 4C2 x 5C1 = 30
3) 3 tech0 businessmen: 4C3 = 4
Total: 144+54+4 = 74
Answer: A
Answer: A
Question: Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is Y?
Options:
A)50+Y/200
B)50+3Y/100
C)50+Y/40
D)100+Y/50
E)100+3A/100
Rationale: 50+Y/40=C
Answer: C
Question: The radius of a circle is increased by 1%. Find how much % does its area increases?
Options:
A)2.71%
B)2.81%
C)2.08%
D)2.01%
E)3.01%
Rationale: r = 100 r = 101
r2 = 10000 r2 = 10201
10000 ---- 201
100 ---- ? => 2.01%
Answer: D
Answer: D
Question: If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Roe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Roe?
Options:
A)15
B)60
C)75
D)90
E)105
Rationale: This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.
Teena covers 55 miles in 60 mins.
Roe covers 40 miles in 60 mins
So teena gains 15 miles every 60 mins
Teena need to cover 7.5 +15 miles.
Teena can cover 7.5 miles in 30 mins
Teena will cover 15 miles in 60 mins
So answer 30+60= 90 mins.D
Answer: D
Question: Sum of ages of two friends is 27 while difference is 3 then their ages are
Options:
A)20 years, 7 years
B)17 years, 15 years
C)17 years, 16 years
D)12 years, 15 years
E)None
Rationale: 12,15
ANSWER:D
Answer: D
Question: In a urban village of india named "owlna" , 70% people have refrigerator , 75% people have television , 65% people got computers and 95% got Air-conditionor. how many people(minimum) got all these luxury.
Options:
A)5%
B)7%
C)3%
D)9%
E)15%
Rationale: A
10%
100 - [ (100-65)+(100-95)+(100-75) +(100-70)]
=100-(30+25+35+5)
=100-95
Answer: A
Question: If y is a positive number and 1/2 the square root of x is the cube root of y, then y=
Options:
A)64
B)32
C)16
D)4
E)1
Rationale: 1/2 the square root of x is cube root of y.
if y= 64..
then 1/2 the square root of y= 4 and cube of y is 64.
Option A.
Answer: A
Question: There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts Y needed to confirm that each of the 5 keys matches each of the 5 locks?
Options:
A)5,15
B)4,15
C)5,10
D)4,10
E)5,20
Rationale: Assume you have locks 1-5 and keys A-E.
Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum.
Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of Y= 4 + 3 + 2 + 1 = 10 attempts.D
Answer: D
Question: Find the area of trapezium whose parallel sides are 28 cm and 18 cm long, and the distance between them is 15 cm.
Options:
A)227
B)299
C)345
D)161
E)212
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (28 + 18) * (15)
= 345 cm2
Answer: C
Answer: C
Question: A number x is 5 times another number y. The percentage that y is less than x is
Options:
A)12.5%
B)87.5%
C)80%
D)11%
E)1%
Rationale: Say y=1 and x=5.
Then y=1 is less than x=5 by (5-1)/5*100=4/5*100=80%.
Answer: C.
Answer: C
Question: A and B’s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?
Options:
A)2777
B)1500
C)2789
D)2776
E)2881
Rationale: (5/100) A = (15/100) B
A = 3B
A + B = 2000
4B = 2000 => B = 500
A = 1500
AnswerD
Answer: D
Question: In an electric circuit, two resistors with resistances 3ohm and 5 ohm are connected in parallel. In this case, if R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of two resistors. What is the value?
Options:
A)15 ohms
B)15/8 ohms
C)1/8 ohms
D)8/15 ohms
E)8 ohms
Rationale: The wording is a bit confusing, though basically we are told that 1/R = 1/3 + 1/5, from which it follows that R=15/8ohms.
Answer: B.
Answer: B
Question: A tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride. The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. If the water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloride stays the same, what will be the concentration of water in the mixture in 6 hours?
Options:
A)18%
B)20%
C)22%
D)24%
E)26%
Rationale: The number of gallons in the tank is (1/4)24 = 6 gallons
The amount of sodium chloride is 0.4(6) = 2.4 gallons
At the start, the amount of water is 0.6(6) = 3.6 gallons
After 6 hours, the amount of water is 3.6 - 0.5(6) = 0.6 gallons
The concentration of water is 0.6 / (2.4+0.6) = 2/10 = 20%
The answer is B.
Answer: B
Question: Think of a number, divide it by 5 and add 6 to it. The result is 65. What is the number thought of?
Options:
A)24
B)77
C)295
D)267
E)29
Rationale: Explanation :
65-6 = 59
59 x 5 = 295
Answer : C
Answer: C
Question: The true discount on a bill of Rs. 2660 is Rs. 360. What is the banker's discount?
Options:
A)Rs. 432
B)Rs. 422
C)Rs. 416
D)Rs. 442
E)None of these
Rationale: Explanation :
F = Rs. 2660
TD = Rs. 360
PW = F - TD = 2660 - 360 = Rs. 2300
True Discount is the Simple Interest on the present value for unexpired time
=>Simple Interest on Rs. 2300 for unexpired time = Rs. 360
Banker's Discount is the Simple Interest on the face value of the bill for unexpired time
= Simple Interest on Rs. 2160 for unexpired time
=360/2300 × 2660 = 0.16 × 2660 = Rs. 416 Answer : Option C
Answer: C
Question: How long will it take for a sum of money to grow from Rs.3000 to Rs.18,000, if it is invested at 5% p.a simple interest?
Options:
A)8 years
B)64 years
C)100 years
D)56 years
E)None
Rationale: In this case, Rs. 3000 has become Rs.18,000.
Therefore, the interest earned = 18,000 – 3000 =15000
Interest for Rs 3000 @ 5% for 1 year = 150
150 - 1
15000 - ? => 100 years
Answer : C
Answer: C
Question: What number has a 1:20 ratio to the number 10?
Options:
A)10
B)1/2
C)2
D)1/4
E)20
Rationale: 1:20 = x: 10
20x = 10; x=10/20
x=1/2
ANSWER:B
Answer: B
Question: A man spends 1/5 of his salary on food, 1/10 of his salary on house rent and 3/5 of his salary on clothes. He still has $18000 left with him. Find his salary.
Options:
A)$100000
B)$200000
C)$140000
D)$180000
E)$250000
Rationale: The expenditure incurred on each item is expressed as part of the total amount (salary), so it is an independent activity.
In general for independent activities
[1 – (x1/y1 + x2/y2 + x3/y3)] × Total amount = Balance amount
[1 – (1/5 + 1/10 + 3/5)] × Total salary = $18000
[1 – 9/10] × Total salary = $18000
Therefore total salary = $18000 × 10 = $180000
Answer: D
Question: Find the greatest common factor (GFC) of 24, 40 and 60.
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: We first write the prime factorization of each given number
24 = 2 × 2 × 2 × 3 = 23*Cubic* × 3
40 = 2 × 2 × 2 × 5 = 23*Cubic* × 5
60 = 2 × 2 × 3 × 5 = 22*square* × 3 × 5
GFC = 22*square* = 4
corect answer is D) 4
Answer: D
Question: If pq = p^3 + q^2 – 2pq, for what value of q is pq equal to p^3 for all values of p?
Options:
A)-2
B)-1
C)0
D)1
E)2
Rationale: C
p3 + q2 â€“ 2pq = p3
=> q2 - 2pq = 0
=> q (q - 2p) = 0
=> q = 0 or q = 2p
im not following the logic you used here.. how did you replace pq with 0 could someone help explain it in MORE DETAI
C
Answer: C
Question: The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?
Options:
A)8
B)9
C)7
D)62
E)2
Rationale: 2x * x = 128 => x= 8
Answer: A
Answer: A
Question: K-numbers are positive integers with only 2's as their digits. For example, 2, 22, and 222 are K-numbers. The K-weight of a number n is the minimum number of K-numbers that must be added together to equal n. For example, the K-weight of 50 is 5, because 50 = 22 + 22 + 2 + 2 + 2. What is the K-weight of 630?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: 630 = 2*222 + (22*8) + 2*5
K weight of 600 = 2 +8+2 = 12
AnswerC
Answer: C
Question: When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [6]*[4] = ?
Options:
A)[12]
B)[44]
C)[45]
D)[88]
E)[90]
Rationale: [6]*[4]=(6/2+1)(4/2+1)
=[12].
Ans-A
Answer: A
Question: The difference between a two-digit number and the number after interchanging the position of the two digits is 63. What is the difference between the two digits of the number?
Options:
A)4
B)7
C)3
D)Cannot be determined
E)None of these
Rationale: Let the two-digit no. be l0x + y.
Then, (10x + y) â€“ (10y + x) = 63
or, 9(x â€“ y) = 63
or, x â€“ y = 7
Answer B
Answer: B
Question: A tree on first day grows 1/2 of its size second day 1/3 of its size on the previous day similarly than 1/4 and so on..U have calculate after how many days the tree will be 100 times of original size.
Options:
A)188 days
B)198 days
C)178 days
D)168 days
E)158 days
Rationale: suppose 'x' is initial size and 'n' is no. of days.
1st day increment in size of tree = (1/2)x
After 1st day , size of tree = x+(1/2)x= (3/2)x
2nd day increment in size of tree = (1/3)*(3/2)x=(1/2)x
After 2nd day , size of tree = (3/2)x+(1/2)x=2x
3rd day increment in size of tree =(1/4)*2x=(1/2)x
After 3rd day , size of tree = 2x+(1/2)=(5/2)x
It is clear that every day tree grows (1/2)x in size.
therefore , according to given condition
x+ (1/2)x*n=100x
n=198 days.
ANSWER:B
Answer: B
Question: A committee of 5 is to be selected from among 5 boys and 5 girls. I how many ways can this be done if the committee is to consist of at-least one Girl?
what is the answer choice and how?
Options:
A)105
B)250
C)230
D)350
E)455
Rationale: I'm sure there is some problem with the question.
R U sure its atleast one boy and not atleast 1 boy and 1 girl?
if its 1 boy and 1 girl
5C1*5C4 + 5C2*5C3 + 5C3*5C2 + 5C4*5C1
5*5 + 10*10 + 10*10 + 5*5
25 + 100 + 100 + 25
250
B
Answer: B
Question: Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
Options:
A)50 m
B)60 m
C)70 m
D)80 m
E)90 m
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
Answer: B
Question: The number of arrangements that can be made with the letters of the word LUCK so that the vowels occupy the even places?
Options:
A)5
B)3
C)6
D)1
E)2
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 1 even places in 1! i.e., 1 ways. While the consonants can be arranged among themselves in the remaining 3 places in 3! i.e., 6 ways.
Hence the total ways are 1 * 6 = 6.
Answer:C
Answer: C
Question: A boatman can row 3 km against the stream in 36 minutes and return in 18 minutes. Find the rate of current ?
Options:
A)7/2 kmph
B)2.5 kmph
C)5/2 kmph
D)1/2 kmph
E)2/2 kmph
Rationale: Explanation:
Speed in upstream = Distance / Time = 3 x 60/36 = 5 km/hr.
Speed in downstream = 3 x 60/18 = 10 km/hr
Rate of current = (10-5)/2 = 2.5 km/hr.
Answer: B
Answer: B
Question: A space shuttle orbits the earth at about 4 kilometers per second. This speed is equal to how many kilometers per hour?
Options:
A) 480
B) 14,400
C) 24,200
D) 28,800
E) 48,000
Rationale: Seconds in 1 hours:
60s in 1 min
60 min in 1 hr
60*60=3600 sec in 1 hr
4*3600=14,400
Answer: B
Answer: B
Question: Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
Options:
A)Rs. 1(1/9)
B)Rs. 2(2/9)
C)Rs. 2(1/9)
D)Rs. 2(2/7)
E)Rs. 2(2/5)
Rationale: Here r = 10 % ,x = 100 and A = 5 kg
Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)
B
Answer: B
Question: There are 16 bees in the hive , then 5 more fly. How many bees are there in all?
Options:
A)20
B)33
C)12
D)17
E)25
Rationale: 16+5=20 . Answer is A.
Answer: A
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
Options:
A)288
B)150
C)77
D)166
E)1812
Rationale: 1/2 * 20(9 + 6) = 150 cm2
Answer: B
Answer: B
Question: Dhoni weighs twice as much as Nameetha. Nameetha's weight is 60% of Bima's weight. Dravid weighs 45% of Leela's weight. Leela weighs 25% of Dhoni's weight. Who among these 5 persons weighs the least?
Options:
A)Dhoni
B)Bima
C)Leela
D)Dravid
E)Nameetha
Rationale: if
Bima weight = x
we get
Nameetha's weight = 0.6x
Dhoni's weight = 1.2x
Leela's weight = 0.3x
and Dravid's weight = 0.135x
Answer : D
Answer: D
Question: The average weight of 10 persons increases by 6.3 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
Options:
A)176 kg
B)80 kg
C)185 kg
D)90 kg
E)128 kg
Rationale: Solution
Total weight increased	= (10 x 6.3)kg
= 63 kg.
Weight of new person	= (65 + 63)kg
= 128 kg.
Answer E
Answer: E
Question: 40, 45, 50, 55, 60, 75, 75, 80, 100, 100.
The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 20.4, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: The average of {40, 45, 50, 55, 60, 75, 75, 80, 100, 100} is 68.
1 standard deviation below the mean is 68 - 20.4 = 47.6. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean.
Answer B.
Answer: B
Question: The average of 9 numbers is 23. If each number is increased by 4, what will the new average be?
Options:
A)25
B)26
C)27
D)28
E)29
Rationale: Sum of the 9 numbers = 207
If each number is increased by 4, the total increase =
4 * 9 = 36
The new sum = 207 + 36 = 243 The new average = 243/9 = 27.
ANSWER:C
Answer: C
Question: Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.14 per cubic meter?
Options:
A)1386
B)2799
C)2890
D)1485
E)2780
Rationale: 22/7 * 14 * 3/2 * 3/2
= 99 m2
99 * 14
= 1386
Answer:A
Answer: A
Question: A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
Options:
A)18
B)77
C)66
D)55
E)12
Rationale: 8/12 + 6/x = 1
X = 18 days
Answer:A
Answer: A
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time cistern will get filled ?
Options:
A)7 hours
B)7.1 hours
C)7.2 hours
D)7.3 hours
E)None of these
Rationale: Explanation:
When we have question like one is filling the tank and other is empting it, then we subtraction as,
Filled in 1 hour = 1/4
Empties in 1 hour = 1/9
Net filled in 1 hour = 1/4 - 1/9
= 5/36
So cistern will be filled in 36/5 hours i.e. 7.2 hours
Option C
Answer: C
Question: Replace the ? by the correct Mathematics symbol to make the expression true
15 ? 3 ? 3 ? 5 = 10
Options:
A)15 ÷ 3 x 3 - 5 = 10
B)15 + 3 ÷ 3 + 5 = 10
C)15 x 3 + 3 + 5 = 10
D)15 x 3 ÷ 3 + 5 = 10
E)15 x 3 ÷ 3 + 6 = 10
Rationale: Answer : A
Answer: A
Question: The cube root of .000216 is:
Options:
A)0.6
B)0.06
C)0.9
D)0.2
E)0.61
Rationale: Answer: B) .06
Answer: B
Question: Each month, after Jill pays for rent, utilities, food, and other necessary expenses, she has one fifth of her net monthly salary left as discretionary income. Of this discretionary income, she puts 30% into a vacation fund, 20% into savings, and spends 35% on eating out and socializing. This leaves her with $108 dollar, which she typically uses for gifts and charitable causes. What is Jill’s net monthly salary?
Options:
A)$2400
B)$3200
C)$6000
D)$3600
E)$9600
Rationale: let x be the monthly salary
15%of 1/5*x=108
x=3600
answer D
Answer: D
Question: The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average?
Options:
A)72
B)77
C)26
D)27
E)29
Rationale: Sum of the marks for the 12 students
= 12 * 36 = 432. The marks of each student are doubled, the sum also will be doubled.
The new sum = 432 * 2 = 864. So, the new average
= 864/12 = 72.
Answer:A
Answer: A
Question: How many ways are there to split a group of 8 boys into two groups of 4 boys each? (The order of the groups does not matter)
Options:
A)24
B)35
C)43
D)60
E)72
Rationale: 8C4 = 70
If we consider these groups, each group will be counted twice.
The number of ways to choose 2 groups of 4 is 70/2 = 35
The answer is B.
Answer: B
Question: A man swims downstream 65 km and upstream 35 km taking 5 hours each time; what is the speed of the current?
Options:
A)2
B)3
C)5
D)7
E)9
Rationale: 65 --- 5 DS = 13
? ---- 1
35 ---- 5 US = 7
? ---- 1 S = ?
S = (13 - 7)/2 = 3
Answer: B
Answer: B
Question: x, a, z, and b are single digit positive integers. x = 1/8 a. z = 1/8 b. (10a + b) – (10x + z) could NOT equal
Options:
A)28
B)35
C)49
D)63
E)55
Rationale: a=8x , b =8z therefore(8x.10+8z) - (10x +z) = (8-1) (10x+z) =7.(10x+Z)
number should be divisible by 7
E
Answer: E
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)3 2/5 Km
C)3 3/5 Km
D)4 1/5 Km
E)5 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
A)
Answer: A
Question: The average of fifteen results is 593 and that of the first fourteen is 594. The fifteenth result is?
Options:
A)575
B)602
C)579
D)586
E)592
Rationale: 15 * 593 â€“ 14 * 594 = 579
Answer: C
Answer: C
Question: Sequence A consists of 16 consecutive integers. If -6 is the least integer in sequence A, what is the range of the positive integers in sequence A?
Options:
A) 16
B) 15
C) 9
D) 8
E) 7
Rationale: Since set A consists of 16 consecutive integers and -6 is the least integer then set A is consecutive integers from -6 to 9, inclusive: 9-(-6)+1=16.
The range of positive integers in sequence A is 9-1=8.
Answer: D.
Answer: D
Question: The entire range of values of x is marked by the dark region on the number line, as shown above. Which of the following expressions describes the range of values of x?
Options:
A)(3+x)(2−x) ≤ 0
B)(3−x)(2+x) ≥ 0
C)(x−3)(x+2) ≤ 0
D)(x+3)(2−x) ≥ 0
E)(3−x)(2−x) ≥ 0
Rationale: Given: x≥−3x≥−3 and x≤2 x≤2
(x+3)≥0(x+3)≥0 and (x−2)≤0(x−2)≤0
(x+3)≥0(x+3)≥0 and (2−x)≥0(2−x)≥0
Answer: D
Answer: D
Question: If n is an integer and n^4 is divisible by 9, which of the following could be the remainder when n is divided by 9?
Options:
A)1
B)3
C)5
D)6
E)8
Rationale: option 1
Remainder 1 means 9+1=10
n^4= 10^4= 10*10*10*10/9 is not an integer
option 2
Remainder 3 means 9+3=12
n^4= 12*12*12*12/9 is an integer means n^4 is divisible by 9 if we take n=3
so B is correct
Answer: B