mathewhe/aqua_rat huggingface dataset:
Question: Which of the following numbers is the biggest => [-5/7 , -7/8 , -9/10 , -12/13 , -34/35]
(A) A)-5/7
(B) B)-7/8
(C) C)-9/10
(D) D)-12/13
(E) E)-34/35
Rationale: If we observe all the fractions just differ by one i.e denominator vs numerate.. in such case the biggest will be with large values... here all values are with -ve value...the least value is biggest. i.e. -5/7..
Hence A is correct answer...
Answer: (A) A)-5/7
Question: What is the difference between 38% of 80 nd 12% of 160.
(A) 11.3
(B) 12.4
(C) 12.7
(D) 11.2
(E) 10.3
Rationale: (38/100) * 80 â€“ (12/100) * 160
30.4 - 19.2 = 11.2
Answer: D
Answer: (D) 11.2
Question: What is the minimum value of |x-4| + |x+8| + |x-5| ?
(A) -13
(B) 13
(C) 5
(D) 7
(E) 8
Rationale: A cannot be the answer as all the three terms are in modulus and hence the answer will be non negative.
|x-4| >= 0 --> Minimum occurs at x = 4
|x+8| >= 0 --> Minimum occurs at x = -8
|x-5| >= 0 --> Minimum occurs at x = 5
x = -8 --> Result = 12 + 0 + 13 = 25. Also any negative value will push the combined value of |x-4| + |x-5| to a value > 9.
x = 4 --> Result = 0 + 12 + 1 = 13
x = 5 --> Result = 1 + 13 + 0 = 14
x = 8 --> Result = 4 + 16 + 3 = 23
So minimum value of the expression occurs at x = 4 and the resultant value = 13
Answer: B
Answer: (B) 13
Question: Linda bought 3 notebooks at $1.20 each; a box of pencils at $1.50 and a box of pens at $1.70. How much did Linda spend?
(A) $6.80
(B) $2.80
(C) $4.80
(D) $7.80
(E) $8.80
Rationale: Linda spent
1.20 ? 3 = $3.60 on notebooks
The total amount of money that Linda spent is equal to
3.60 + 1.50 + 1.70 = $6.80
correct answer A
Answer: (A) $6.80
Question: If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (3x + 2y) is positive integer II. (xy)^2 is positive integer III. (y^2 - x) is even integer
(A) I only
(B) III only
(C) II only
(D) I,III only
(E) none of these
Rationale: I. It is true if 3x < 2y
II. It is always positive
III. It is not always true
Answer : C
Answer: (C) II only
Question: Pary,INC recently conducted a survey and found that 75,000 of its customers live in rural areas. if the number of it customers who live in urban areas is 200 percents grater than the numbers of customers who live in rural areas, how many of Pary,INC customers live in urban areas ?
(A) 200,000
(B) 216,000
(C) 225,000
(D) 480,000
(E) 540.0
Rationale: Let's say that we have a starting value of X...
100% of X = X
100% MORE than X = X + X = 2X
200% MORE than X = X + 2X = 3X
300% MORE than X = X + 3X = 4X
Etc.
Here, we're told that 75,000 customers live in rural areas and the number who live in urban areas is 200% GREATER than the number who live in rural areas. That means that the number who are in urban areas is 3 times the number in rural areas...
3(75,000) = 225,000
Final Answer:C
Answer: (C) 225,000
Question: A sum of Rs. 427 is to be divided among A, B and C in such a way that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal. The share of C is
(A) 82
(B) 83
(C) 84
(D) 85
(E) 86
Rationale: A + B + C = 427
3A = 4B = 7C
=> (7C/3) + (7C/4) + C = 427
=> C = 84
ANSWER:C
Answer: (C) 84
Question: A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:
(A) 3
(B) 5
(C) 9
(D) 11
(E) 12
Rationale: Explanation:
Let the ten's digit be x and unit's digit be y.
Then, number 10x + y.
Number obtained by interchanging the digits = 10y + x.
(10x + y) + (10y + x) = 11(x + y)
which is divisible by 11.
ANSWER IS D
Answer: (D) 11
Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for four years?
(A) 29893
(B) 27773
(C) 29989
(D) 28800
(E) 29883
Rationale: Simple interest = (18000 * 4 * 15)/100 = Rs. 10800
Amount = P + I = 18000 + 10800 = Rs. 28800
Answer: D
Answer: (D) 28800
Question: How many positive integers less than 100 are there such that they are multiples of 8 or multiples of 7 but not both?
(A) 21
(B) 22
(C) 25
(D) 24
(E) 31
Rationale: for 8: 8...100=8*12
for 7: 7...98=7*14
but there is one integer 8*7. so
N=(12-1)+(14-1)=24
D
Answer: (D) 24
Question: There are 11 dozen mangoes in a box. If there are 39
such boxes, how many mangoes are there in all the
boxes together?
(A) 516
(B) 5148
(C) 6192
(D) 628
(E) None
Rationale: Number of mangoes = 11 dozens
= 12 × 11 = 132
∴ Number of mangoes in 39 boxes
= 39 × 132 = 5148
Answer B
Answer: (B) 5148
Question: In an examination 35% of the students passed and 455 failed. How many students appeared for the examination?
(A) 540
(B) 400
(C) 700
(D) 650
(E) 840
Rationale: Let the number of students appeared be x
then, 65% of x = 455
65x/100 = 455
x = 455*100/65 = 700
Answer is C
Answer: (C) 700
Question: 14, 28, 20, 40, 32, 64, ?
(A) 43
(B) 25
(C) 58
(D) 47
(E) 56
Rationale: E
56
This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8.
Answer: (E) 56
Question: If cement, gravel and sand are to be mixed in 7:10:13 and 5 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available.
(A) 35 7/8
(B) 36
(C) 21 3/7
(D) 34 5/7
(E) 34 6/7
Rationale: Cement:Gravel:Sand = 7:10:13 --> total of 7+10+13 = 30 parts.
If we use 8 tons of cement, then we'll get 5/7*30 = 21 3/7 tons of mixture.
Answer: C.
Answer: (C) 21 3/7
Question: A person crosses a 1000 m long street in 10 minutes. What is his speed in km per hour?
(A) 7.1
(B) 8.2
(C) 4.6
(D) 6.0
(E) 12.8
Rationale: distance = 1000 meter
time = 10 minutes = 10 x 60 seconds = 600 seconds
Speed = distance/time=1000/600=1.67m/s=1.67Ã—18/5 km/hr=6.0 km/hr
Answer :D
Answer: (D) 6.0
Question: If f(y)=y^2 and y is a positive integer, which of the following CANNOT be the value of f(f(y))?
(A) 1
(B) 144
(C) 81
(D) 16
(E) 256
Rationale: f(y)=y^2
f(f(y)) = (y^2)^2
=y^4
A. 1 , y=1
D. 16 , y=2
C. 81 , y=3
B. 144
f(y)=12
Square root of 12 is not a positive integer . Hence 144 can not be the value of f(f(y)) .
E. 256 , y=4
Answer B
Answer: (B) 144
Question: The sum of two numbers is twice their difference. If one of the numbers is 10, the other number is
(A) 3 1/3
(B) 30
(C) −3 1/3
(D) a or b
(E) None
Rationale: Explanation:
Let the other number be a.
Given that, 10+a=2(a−10)⇒a=30
or if the other number is less than 10, 10+a=2(10−a)⇒a=10/3=3 1/3
Correct Option: D
Answer: (D) a or b
Question: If the positive integer x is a multiple of 9/15 and the positive integer y is a multiple of 5/3, then xy must be a multiple of which of the following?
I. 5
II. 3
III. 1
(A) II only
(B) I and II only
(C) I only
(D) III only
(E) I, II, and III
Rationale: x=9/15a
y=5/3b
xy=3/3ab=ab
where a,b are integers
Hence , xy will always be divisible by 1.
D is the answer.
Answer: (D) III only
Question: A girl scout was selling boxes of cookies. In a month, she sold both boxes of chocolate chip cookies ($1.25 each) and boxes of plain cookies ($0.75 each). Altogether, she sold 1,585 boxes for a combined value of $1,588.25. How many boxes of plain cookies did she sell?
(A) 0
(B) 233
(C) 500
(D) 695
(E) 786
Rationale: Let #plain cookies sold be X then #chocolate cookies = (total cookies-X)
Equating for X
(0.75)*X +(1.25)*(1585-X)=1588.25
=>x=786
First get the difference of the revenue to the number of boxes.
1588.25-1585=3.25
Now you know that the difference between plain cookies boxes and chocolate cookies boxes is small.
We now divide the revenue by two.
1588.25/2=~794
Because the difference between the possible answers is big, this leaves us with choice E.
Answer: (E) 786
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 500 m long?
(A) 176 Sec
(B) 190 Sec
(C) 170 Sec
(D) 267 Sec
(E) 276 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1700 m
T = D/S
T = 1700/10
T = 170 Sec
Answer:C
Answer: (C) 170 Sec
Question: A scale 7 ft. 6 inches long is divided into 5 equal parts. Find the length of each part.
(A) 20 inches
(B) 77 inches
(C) 66 inches
(D) 18 inches
(E) 66 inches
Rationale: Explanation:
Total length of scale in inches = (7*12) + 6 = 90 inches
Length of each of the 5 parts = 90/5 = 18 inches
ANSWER:D
Answer: (D) 18 inches
Question: The average weight of 10 person's increases by 4 kg when a new person comes in place of one of them weighing 70kg. What is the weight of the new person?
(A) 85
(B) 86.5
(C) 90
(D) 88.5
(E) 110
Rationale: Total increase in weight =10 x 4 = 40
If x is the weight of the new person, total increase in weight = x−70
=> 40= x - 70
=> x = 40+70 = 110
ANSWER:E
Answer: (E) 110
Question: A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?
(A) 17 kmph
(B) 24 kmph
(C) 16 kmph
(D) 19 kmph
(E) 11 kmph
Rationale: Distance from A and B be 'd'
Average Speed = total distance/total time
Average Speed = (2d)/[(d/20) + (d/30)]
= (2d)/[5d/60) => 24 kmph.
Answer:B
Answer: (B) 24 kmph
Question: If 8^x = 2^15, what is x?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 2^3x= 2^15
3x=15, therefore x=5
Answer D
Answer: (D) 5
Question: The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 588, Krishan has ?
(A) s. 2890
(B) s. 2330
(C) s. 1190
(D) s. 3468
(E) s. 2680
Rationale: Ram : Gopal = 7 : 17 = 49 : 119
Gopal : Krishan = 7 : 17 = 119 : 289
Ram : Gopal : Krishan = 49 : 119 : 289
Ram : Krishan = 49 : 289
Thus, 49 : 289 = 588 : N
&there N = 289 x 588 / 49
= Rs. 3468
Answer :D
Answer: (D) s. 3468
Question: A waiter's salary consists of his salary and tips. During one week his tips were 9/4 of his salary. What fraction of his income came from tips ?
(A) 4/9
(B) 5/4
(C) 9/13
(D) 5/9
(E) 6/9
Rationale: Income = salary (s) +tips = s + s*9/4 = s*13/4
Tips = s*9/4
fraction of his income came from tips = (s*9/4)/(s*13/4)= 9/13
ANSWER:C
Answer: (C) 9/13
Question: A trumpet section includes seven musicians. If they hold an audition to determine chair order within the section, and there are to be no ties, how many distinct chair orders can result?
(A) 240
(B) 125
(C) 5040
(D) 100
(E) 25
Rationale: We have a word problem using permutations. We must identify the number of total items in the group. There are seven possible musicians who could be placed in the first chair, six possible musicians for the second, five for the third, four for the fourth, and three for the fifth, and two for the sixth and one for the seventh. To determine the number of possible orderings, we multiply these numbers, which we can express as 7!. Now 7! = (7)(6)(5)(4)(3)(2)(1) = 5040=C
Answer: (C) 5040
Question: Which of the following numbers is two more than the square of an odd integer?
(A) 14,115
(B) 14,163
(C) 14,577
(D) 14,737
(E) 14,981
Rationale: If a square has an odd unit's digit, then its ten's digit must be even.
Only 14,163-2 = 14,161 satisfies this condition.
The answer is B.
Answer: (B) 14,163
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 600 m long?
(A) 80sec
(B) 84sec
(C) 90sec
(D) 94sec
(E) 100sec
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 600)/10 = 84 sec.
Answer:B
Answer: (B) 84sec
Question: A certain company consists of 3 managers and 8 non-managers. How many different teams of 3 employees can be formed in which at least one member of the team is a manager and at least one member of the team is not a manager? (Two groups are considered different if at least one group member is different)
(A) 84
(B) 108
(C) 135
(D) 270
(E) 990
Rationale: Total # of teams of 3 possible is C311=165
# of teams with only managers or only non-managers is: C33+C38=1+56=57;
# of teams of 3 with at least one manager or at least one non-manager is: 165-57=108.
ANSWER:B
Answer: (B) 108
Question: A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
(A) 33
(B) 38
(C) 87
(D) cannot be determined
(E) 282
Rationale: Explanation:
We need to know the S.I, principal and time to find the rate. Since the principal is not given, so data is inadequate.
Answer: D)
Answer: (D) cannot be determined
Question: The bankerâ€™s discount on Rs. 1600 at 6% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is :
(A) 2 months
(B) 4 months
(C) 6 months
(D) 10 months
(E) None
Rationale: Sol.
S.I. on Rs. 1600 = R.D. on Rs. 1680.
âˆ´ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is S.I. on Rs. 1600 at 6%.
âˆ´ Time = [100 * 80 / 1600 * 6] year = 5/6 year = 10 months.
Answer D
Answer: (D) 10 months
Question: One vessel contains a mixture of 5 parts pure wine and 3 parts soda, whereas the other vessel contains a mixture of 9 parts pure wine and 5 parts soda. Compare the strength of the wine.
(A) 35;36
(B) 7 : 8
(C) 7 : 4
(D) 14 : 5
(E) None of these
Rationale: 5/8 : 9/14
LCM of 8,14 = 56
(5/8)*56 : (9/14)*56
35:36
Answer is A
Answer: (A) 35;36
Question: Currently, y percent of the members on the finance committee are women and next month, z percent of the men on the finance committee will resign. If no other personnel changes occur, then after the resignations next month, the men who remain on the finance committee will represent what percent of the total finance committee members?
(A) (100)(100 - z)(100 - y)/(100^2 - z(100 - y))
(B) (100 - z)(100 - y)/100
(C) (100 - z)(100 - y)
(D) zy/100 - z
(E) z(100 - y)/100
Rationale: Let's say that there are a total of 100 members
Let's also say that y = 50
So there are 50 men
Now z = 10 so 45 men are left
(45/95)*100 = 9/19 *100 = 900/19
Now let's plug answer choices
Target 900/19
Inputs
y=50
z=10
Only A gives the correct answer
Answer: (A) (100)(100 - z)(100 - y)/(100^2 - z(100 - y))
Question: Carina has 55 ounces of coffee divided into 5- and 10-ounce packages. If she has 2 more 5-ounce packages than 10-ounce packages, how many 10-ounce packages does she have?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3
Rationale: Lets say 5 and 10 ounce packages be x and y respectively.
Given that, 5x+10y=55 and x=y+2. What is the value of y.
Substituting the x in first equation, 5y+10+10y=55 ->y=45/15.=3
E
Answer: (E) 3
Question: A wooden box of dimensions 8 m x 7 m x 6 m is to carry rectangularboxes of dimensions 2 cm x 7 cm x 3 cm. The maximum number ofboxes that can be carried in the wooden box, is
(A) 8000000
(B) 1000000
(C) 7500000
(D) 1200000
(E) None of these
Rationale: Explanation: Number = (800*700*600)/2*7*3 = 8000000 Answer: A
Answer: (A) 8000000
Question: Bruce purchased 8kg of grapes at the rate of 70 per kg and 11 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
(A) A)1040
(B) B)1165
(C) C)1055
(D) D)1065
(E) E)1075
Rationale: Cost of 8 kg grapes = 70 × 8 = 560.
Cost of 11 kg of mangoes = 55 × 11 = 605.
Total cost he has to pay = 560 + 605 = 1165
B
Answer: (B) B)1165
Question: As a treat for her two crying children, a mother runs to the freezer in which she has two cherry ice pops, three orange ice pops, and five lemon-lime ice pops. If she chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one invariably being jealous of the other and getting even more upset, what is the probability that she has to return to the freezer to make sure that they each receive the same flavor?
(A) 1/9
(B) 1/6
(C) 5/18
(D) 31/360
(E) 5/6
Rationale: Probability of not getting the same flavor ->
Favorable -> Cherry - orange [ 2C1 * 3C1 [or simply 2*3 ] or Cherry - lemon [ 2*5] or orange - lemon [3*5]
Prob = (2*3 + 2*5 + 3*5 ) / 9C2 = 31/360
Answer -> D
Answer: (D) 31/360
Question: Find the number of subsets of the set {1,2,3,4,5,6,7,8,9,10,11} having 4 elements.?
(A) 1320
(B) 660
(C) 165
(D) 330
(E) None of these
Rationale: Explanation :
Here the order of choosing the elements doesn’t matter and this is a problem in combinations.We have to find the number of ways of choosing 4 elements of this set which has 11 elements.This can be done in:11C4=11*10*9*81*2*3*4= 330 ways
Answer : D
Answer: (D) 330
Question: In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (3,3) and if point A is equidistant from points O and B and the area of the triangle OAB is 16, which of the following are the possible coordinates of point A.
(A) (-2,6)
(B) (0,4)
(C) (2,-6)
(D) (2,6)
(E) (4,0)
Rationale: Area.pngSince A is equidistant from points O and B, then it must be somewhere on the green line (perpendicular bisector of OB).
(2,-6) and (2,6) are not on that line. If A is at (0,3) or (3,0), then the area is 1/2*3*3=9/2. Thus A must be at (2,6).
Answer: D.
Answer: (D) (2,6)
Question: In 1990 the budgets for projects Q and V were $660,000 and $860,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V ?
(A)  1992
(B)  1993
(C)  1994
(D)  1995
(E)  1996
Rationale: Let the no of years it takes is x.
660+30x = 860-10x --> 40x = 200 and x=5.
Thus, it happens in 1995.
D.
Answer: (D)  1995
Question: The sum of one-half, one-third and one-fourth of a number exceeds the number by 12. The number is
(A) 144
(B) 154
(C) 90
(D) 174
(E) 184
Rationale: x/2+x/3+x/4=x+12
13x/12=x+12
x=144
ANSWER:A
Answer: (A) 144
Question: 12 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 27 cm height. What is the diameter of each sphere?
(A) 2 cm
(B) 4 cm
(C) 6 cm
(D) 8 cm
(E) 10 cm
Rationale: Volume of cylinder = pi*r^2*h
Volume of a sphere = 4*pi*R^3 / 3
12*4*pi*R^3 / 3 = pi*r^2*h
R^3 = r^2*h / 16 = 27 cm^3
R = 3 cm
D = 6 cm
The answer is C.
Answer: (C) 6 cm
Question: If x*y = xy – 2(x + y) for all integers x and y, then 5* (–3) =
(A) –19
(B) –11
(C) –4
(D) 4
(E) 16
Rationale: 5*(-3) = 5*(-3) - 2 (5 + (-3) ) = -15 -4 = -19
Option (A)
Answer: (A) –19
Question: How many numbers from 10 to 100 are exactly divisible by 9?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 14
Rationale: 10/9 = 1 and 100/9 = 11 ==> 11 - 1 = 10. Therefore 10 digits
B)
Answer: (B) 10
Question: If sum of the first 11 terms of arithmetic progression equals that of the first 19 terms, then what is the sum of the first 30 terms?
(A) 0
(B) -1
(C) 1
(D) Not unique
(E) None of these
Rationale: Explanation :
Given,
t1 + t2 + ........t11 = t1 + t2 + ........t19 (for an AP)
=> (11/2) [ 2a + (11-1)d = (19/2) [ 2a + (19-1)d ]
=> 22 a + 110d = 28 a + 342 d
=> 16 a + 232 d = 0
=> 2a + 29 d = 0
=> (30/2)[ 2a + (30-1)d = 0.
S30 terms = 0.
Answer : A
Answer: (A) 0
Question: There are two sections B and C of a class, consisting of 46 and 54 students respectively. If the average weight of sections B is 50 kg and that of sections C is 45 kg. Find the average weight of the whole class
(A) 47.3
(B) 48.3
(C) 49.3
(D) 50.3
(E) None
Rationale: Solution
Total weight of(46+54)Students	= (46x50+54x45)Kg
= 4730 kg.
Average weight of the whole class	= (4730 / 100)
= 47.30.
Answer A
Answer: (A) 47.3
Question: If 8000 books need to be placed in boxes and each box can contain at most 9 books. How many books will be in the last unfilled box?
(A) 8 books
(B) 9 books
(C) 1 book
(D) 5 books
(E) 4 books
Rationale: The number of books that can be placed in boxes of 9 books is the first number that is divisible by 9 that occurs before 8000.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 8000 = 8 and 0 is divisible by 9.
Hence, we need to remove 8 to this number for it to be divisible by 9
Correct Option:A
Answer: (A) 8 books
Question: There are 193 items that are members of set U. Of these items, 41 are members of set B, 59 are not members of either of set A or set B, and 23 are members of both sets A and B. How many of the members of set U are members of set A ?
(A) 116
(B) 85
(C) 94
(D) 98
(E) 108
Rationale: You had the answer almost right. The x = 93 refers to ONLY set A.
However what's being asked is how many members are part of set A. This will include:
1. Only Set A
2. Set A and Set B
So the answer is Set A = 93 + Set AB = 93+23 = 116
A
Answer: (A) 116
Question: Sand is poured into a box so that the box is being filled at the rate of 4 cubic feet per hour. If the empty rectangular box is 7 feet long, 6 feet wide, and 2 feet deep, approximately how many hours does it take to fill the box?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: The volume the box is: length*width*depth = 7*6*2= 84 cubic feet.
84 cubic feet / 4 cubic feet per hour = 21 hours.
It will take 21 hours to fill the box.
The answer is B.
Answer: (B) 21
Question: While working alone at their respective constant rates, server M uploads 480 files in 4 hours and server Y uploads 480 files in 8 hours. If all files uploaded by these servers are the same size, how long would it take the two servers, working at the same time and at their respective constant rates, to process a total of 480 files?
(A)  2 hr
(B)  2hr 20 min
(C)  2hr 40 min
(D)  5 hr 40 min
(E)  6hr
Rationale: Server M processes 480/4 files per hour = 120 per hour
Server Y processes 180/8 files per hour = 60 per hour
Total files processed per hour when M and Y work together = 120+60 per hour = 180 files per hour
480/180 = 2 2/3 hours=C
Answer: (C)  2hr 40 min
Question: N= 1!+2!+3!.....+10!. what is the last digit of N^N?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: as you see 5! till 10 ! each unit digit is zero.
so 1!+2!+3!+4! =33
so unit digit 3+ 0 =3
N=3
N^N= 3^3=27
so last digit is 7.
ANSWER:E
Answer: (E) 7
Question: In the xy-coordinate system, if (m, n) and (m 1 2, n 1 k) are two points on the line
with the equation x 5 2y 1 5, then k 5
(A) 1/2
(B) 1
(C) 2
(D) 5/2
(E) 4
Rationale: Step 1: Analyze the Question
For any question involving the equation of a line, a good
place to start is the slope-intercept form of the line,
y = mx 1 b. Remember that if you have two points on a
line, you can derive the entire equation, and if you have an
equation of the line, you can calculate any points on that
line.
Step 2: State the Task
We are solving for k, which is the amount by which the
y-coordinate increases when the x-coordinate increases
by 2.
Step 3: Approach Strategically
The slope of a line is the ratio between the change in y and
the change in x. In other words, every time the x-coordinate
increases by 1, the y-coordinate increases by the amount
of the slope.
The equation of the line in the question stem is defined as
x = 2y + 5. We must isolate y to have slope-intercept form:
So the slope of this line is 1/2 . This means that for every
change of +1 in the x direction, there is a change of + 1/2
in the y direction. Then we know that, because there is an
increase in 2 units in the x direction when moving from
m to m + 2, there must be a change of 1 unit in the y
direction when moving from n to n + k. So k = 1.
Since there are variables that eventually cancel (m and n
are not part of the answers), we can Pick Numbers. Let’s
say that you choose the y-coordinate of the point (m, n) to
be 0 to allow for easier calculations. Using the equation
we’re given to relate x- and y-coordinates, we can calculate
the x-coordinate:
So (m, n) is the point (5, 0).
Now we’ll plug our values of m and n into the next point:
(m + 2, n + k). That yields (7, k). All we have to do is plug
an x-coordinate of 7 into the equation to solve for k, the
y-coordinate:
Answer is B
Answer: (B) 1
Question: Sarah is driving to the airport. After driving at 20 miles per hour for one hour, she realizes that if she continues at that same average rate she will be an hour late for her flight. She then travels 50 miles per hour for the rest of the trip, and arrives 30 minutes before her flight departs. How many miles did she drive in all?
(A) 140
(B) 175
(C) 210
(D) 70
(E) 280
Rationale: After driving at 20 miles per hourfor one hour, this distance left to cover is d-20. Say this distance is x miles.
Now, we know that the difference in time between covering this distance at 20 miles per hour and 50 miles per hour is 1+ 1/2 = 3/2 hours.
So, we have that x/20 - x/50 = 3/2 --> 5x/100 - 2x/100 = 3/2 --> 3x/100 = 3/2 --> x = 50.
Total distance = x + 20 = 70 miles.
Answer: D
Answer: (D) 70