mathewhe/aqua_rat huggingface dataset:
Question: To fill a cistern, pipes A,B and C take 20 minutes, 15 minute and 12 minutes resp. The time in minutes that the three pipes together will take to fill the cistern is
(A) 5
(B) 6
(C) 8
(D) 3
(E) 9
Rationale: A
5
Answer: (A) 5
Question: A factory produces x widgets per day. The factory's fixed costs are $8000 per day. The price per widget is $70 and the variable costs are $30 per widget. How many widgets need to be produced for profits of $5440 a day?
(A) 42.33
(B) 90.33
(C) 168
(D) 224
(E) 311
Rationale: profits=5440=40x-8000 --> x=311
Answer E.
Answer: (E) 311
Question: Excluding stoppages, the speed of a bus is 58 kmph and including stoppages, it is 40 kmph. For how many minutes does the bus stop per hour?
(A) 19
(B) 19.13
(C) 10.5
(D) 11.35
(E) None of these
Rationale: Due to stoppages, it covers 18 km less.
Time taken to cover 18 km = ((18/58)Ã—60) = 19 min.
Option(A) is correct
Answer: (A) 19
Question: If (2^17)(25^S) = 5(10^m) what is the value of m ?
(A) 7
(B) 8
(C) 15
(D) 16
(E) 17
Rationale: given
2^17 * 25^s = 5 * 10^2
=> 2^17 * 5^(2s) = 2^m * 5^(m+1)
Ans E
on comparing the power of 2 => m=17
Answer: (E) 17
Question: If f(x)=4x−1 and g(x)=2x+6 for all integers, which of the following is a possible value of g(f(x))?
(A) -23
(B) -17
(C) 0
(D) 8
(E) 20
Rationale: g(f(x)) = 2*f(x)+6 = 2*(4x-1)+6 = 8x+4
Of these five options, only 20 has the form 8x+4.
The answer is E.
Answer: (E) 20
Question: If 5 < x < 11 and y = x + 6, what is the greatest possible integer value of x + y?
(A) 25
(B) 26
(C) 27
(D) 28
(E) 29
Rationale: x+y = x+x+6 = 2x+6
We need to maximize this value and it needs to be an integer.
2x is an integer when the decimal of x is .0 or .5
The largest such value is 10.5
Then x+y = 10.5 + 16.5 = 27.
The answer is C.
Answer: (C) 27
Question: Two whole numbers whose sum is 24 is the ratio
(A) 1:3
(B) 2:8
(C) 1:6
(D) 2:3
(E) 2:5
Rationale: A) 1:3
Answer: (A) 1:3
Question: Reena took a loan of 1200 with simple interest for as many years as the rate of interest. If she paid 432 as interest at the end of the loan period, what was the rate of interest?
(A) 6
(B) 3
(C) 7
(D) 8
(E) 9
Rationale: A
6
Let rate = R% and time = R years.
Then, (1200 x R x R)/100 = 432
12R² = 432
R² = 36
R = 6.
Answer: (A) 6
Question: In a recent election, Ms. Robinson received 3200 voters cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. IF N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Mrs. Robbins received?
(A)  0.06N+3200
(B)  0.1N+7200
(C)  0.4N+7200
(D)  0.1N+8000
(E)  0.06N+8000
Rationale: 40% of N are independent voters, hence 60% of N are not independent voters. From this group she received 10% votes so, 0.1*0.6*N plus 3,200 votes from independents: total=0.1*0.6*N+3,200=0.06*N+3,200.
Answer: A.
Answer: (A)  0.06N+3200
Question: If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 140 pounds. What is Leo's current weight?
(A) 80
(B) 90
(C) 100
(D) 110
(E) 120
Rationale: L+K = 140 and so K = 140-L
L+10 = 1.5K = 1.5(140-L)
2.5L = 200
L = 80
The answer is A.
Answer: (A) 80
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
(A) 8
(B) 7
(C) 6
(D) 9
(E) 5
Rationale: 1/10 + 1/15 - 1/x = 1/18
x = 9
Answer:D
Answer: (D) 9
Question: One side of a triangle has length 6 and a second side has length 4. Which of the following could be the area of the triangle?
I. 15
II. 12
III. 5
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II and III
Rationale: The triangle will have a maximum area when it is a right angled triangle
The largest triangle will be formed when 6 and 4 are the base and height of triangle .
Area = 1/2 * 6 * 4 = 12
There is no lower limit on the area of any triangle whose only 2 sides are known.
Then 0 < Area <= 12
The answer is D.
Answer: (D) II and III only
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 22 sec
(B) 16 sec
(C) 17 sec
(D) 88 sec
(E) 12 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
Answer:B
Answer: (B) 16 sec
Question: What is the smallest no. that should be added to 27452 to make it exactly divisible by 9?
(A) 1
(B) 3
(C) 5
(D) 6
(E) 9
Rationale: If a number is divisible by 9, the sum of its digits must be a multiple of 9.
Here, 2+7+4+5+2=20, the next multiple of 9 is 27.
7 must be added to 27452 to make it divisible by 9
E
Answer: (E) 9
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 720 sq. feet, how many feet of fencing will be required?
(A) 34
(B) 40
(C) 68
(D) 88
(E) 92
Rationale: Given that length and area, so we can find the breadth.
Length x Breadth = Area
20 x Breadth = 720
Breadth = 36 feet
Area to be fenced = 2B + L = 2 (36) + 20 = 92 feet answer : E
Answer: (E) 92
Question: There are 100 students in a college class of which 36 are boys studying Tamil & 13 girls not studying Tamil. If there are 55 girls in all, then the probability that a boy picked up at random is not studying Tamil, is
(A) 1/5
(B) 2/5
(C) 3/5
(D) 3/7
(E) 3/8
Rationale: There are 55 girls and 45 boys in the college. Out of 45 boys, 36 are studying Tamil and 9 are not studying Tamil. The probability that a boy picked up at random is not studying Tamil= 9/45 = 1/5
A
Answer: (A) 1/5
Question: The factorial expression 18!/12! is not divisible by which of the following integers?
(A) 3
(B) 5
(C) 19
(D) 14
(E) 9
Rationale: 18!/12! => 18 x 17 x 16 x 15 x 14 x 13
(A) 3 Can divide 18 or 15
(B) 5 Can divide 15
(C) 19 None of the Multiplicands present
(D) 14 Can divide 14
(E) 9 Can divide 9
Hence answer will be (C)
Answer: (C) 19
Question: John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment W that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?
(A) a. 3/5
(B) b.2/3
(C) c.7/10
(D) d.3/4
(E) e.4/5
Rationale: X(10) --- Net(0) --- W(-15) = -15/-10 = 3/2.
So, John invested 3/3+2 = 3/5 of his savings in investment X. Ans (A).
Answer: (A) a. 3/5
Question: If the ratio of x to y is 4 to 5, then (y-x)/(x+y)?
(A) -7/3
(B) -3/7
(C) 1/9
(D) 1
(E) 7/3
Rationale: I believe this problem can be solved using algebra.
The ratio of x to y is 4 to 5 means
(x/y)=(4/5)
Cross-multiply
4x = 5y
x = (4/5)*y
Then, substitute x in the original equation in the problem with the value we just found.
(y - (4/5)*y) / ((4/5)*y + y)
= ((1/5)*y) / ((9/5)*y)
Simplify by canceling the y in the numerator with the y in the denominator.
(1/5) / (9/5)
= (1/5) * (9/7)
The 5s cancel each other out, and you are left with 1/9.
Answer: (C) 1/9
Question: In 10 years, A will be twice as old5as B was 10 years ago. If A is now 7 years older than B, the present age of B is
(A) 35
(B) 37
(C) 39
(D) 41
(E) 42
Rationale: Explanation:
Let B's age = x years.
Then, As age = (x+ 7) years.
(x+7+10)=2(x—10)
hence x=37.
Present age of B = 37 years
Answer: Option B
Answer: (B) 37
Question: The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
(A) 4
(B) 8
(C) 6
(D) 9
(E) 2
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35
So 30x + 35 + 31(x + 1) = > x = 4.
Answer: A
Answer: (A) 4
Question: A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
(A) 14 min
(B) 15 min
(C) 16 min
(D) 30 min
(E) 17 min
Rationale: Part filled by (A + B) in 1 minute = (1/60 + 1/40) = 1/24
Suppose the tank is filled in x minutes.
Then, x/2(1/24 + 1/40) = 1
x/2 * 1/15 = 1 => x = 30 min.Answer: D
Answer: (D) 30 min
Question: A car after covering ½ of a journey of 100 km develops engine trouble and later travels at ½ of its original speed. As a result, it arrives 2 hours late than its normal time. What is the normal speed of the car is?
(A) 15 kmph
(B) 25 kmph
(C) 28 kmph
(D) 29 kmph
(E) 21 kmph
Rationale: B
25 kmph
[50/x + 50/(x/2)] – 100/x = 2
x = 25
Answer: (B) 25 kmph
Question: A sum of money is distributed among A,B,C,D in the proportion of 5:3:2:3. If A gets $1000 more than B, what is the C's share?
(A) $2000
(B) $5000
(C) $8000
(D) $1500
(E) $1000
Rationale: Let the shares of A,B,C,D are 5x,3x,2x,3x
5x-3x = 1000
x = 500
C's share = 2x = $1000
Answer is E
Answer: (E) $1000
Question: How many terms are there in 2, 4, 8, 16,..., 1024?
(A) 14
(B) 11
(C) 12
(D) 10
(E) 8
Rationale: 2, 4, 8, 16, ..., 1024 is a G.P with a =2
and r =4/2 =2
Let the number of terms be n. Then
2 x 2 ^n-1 = 1024
or 2^n-1 = 512 = 2^9
Thus n - 1 =9
n= 10
ANSWER:D
Answer: (D) 10
Question: A trumpet section includes three 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) 120
(D) 100
(E) 6
Rationale: We have a word problem using permutations. We must identify the number of total items in the group. There are three possible musicians who could be placed in the first chair, two possible musicians for the second, one for the third. To determine the number of possible orderings, we multiply these numbers, which we can express as 3!. Now 3! = (3)(2)(1) = 6=E.
Answer: (E) 6
Question: What is the 14th digit to the right of the decimal point in the decimal equivalent of 82/11?
(A) 4
(B) 3
(C) 1
(D) 5
(E) 7
Rationale: 82/11 = 7.4545....
45 is non-repeating terminating decimal.
The 14th digit to the right of decimal point will be 5.
Answer D
Answer: (D) 5
Question: Find the area of a parallelogram with base 22 cm and height 21 cm?
(A) 462 cm2
(B) 478 cm2
(C) 490 cm2
(D) 268 cm2
(E) 668 cm2
Rationale: Area of a parallelogram = base * height
= 22 * 21
= 462 cm2
Answer: A
Answer: (A) 462 cm2
Question: If B takes 20% less time than A, to cover the same distance. What should be the speed of B, if A works at a rate of 10 km/hr?
(A) 12.5 km/hr
(B) 10 km/hr
(C) 15 km/hr
(D) 20 km/hr
(E) 25 km/hr
Rationale: Explanation:
S1 = 10 kmph
if T1 = 100
T2 = 80
10 x 100 = 80 x S2
S2 = 12.5 km/hr
Answer: Option A
Answer: (A) 12.5 km/hr
Question: A sequence of numbers a1a1, a2a2, a3a3,…. is defined as follows: a1=3a1=3, a_2 = 5, and every term in the sequence after a2a2 is the product of all terms in the sequence preceding it, e.g, a3=(a1)(a2)a3=(a1)(a2) and a4=(a1)(a2)(a3)a4=(a1)(a2)(a3). If an=tan=t and n>2n>2, what is the value of an+2an+2 in terms of t?
(A) 4t
(B) t^2
(C) t^3
(D) t^4
(E) t^8
Rationale: An = (A1)(A2)......(An-1) = t
An+1 = t * An = t^2
An+2 = t * An * An+1 = t * t * t^2 = t^4
Answer: D
Answer: (D) t^4
Question: If a boat goes 7km upstream in 42 minutes and the speed of the stream is 3 kmph, then the speed of the boat in still water is ?
(A) 13km/hr
(B) 52km/hr
(C) 85km/hr
(D) 2.8km/hr
(E) 5.98km/hr
Rationale: Rate upsteram =(7/42*60)kmph=10kmph.
speed of the stream =3kmph let speed in still water be xkm/hr. then speed upstream=(x-3)km/hr. x-3=10==>x=13km/hr Answer(A)
Answer: (A) 13km/hr
Question: The ratio between speed of the two trains is 7:8. If the 2nd train runs 400 km in 4 hrs, what is the speed of the 1st train?
(A) 87.9
(B) 87.5
(C) 87.7
(D) 87.6
(E) 43.3
Rationale: Answer: b
Explanation:
Speed of 2nd train = 400/4 = 100 kmph
Since the ratios are in 7 : 8
Speed of First train = 7/8 × 100 = 87.5 kmph
Answer:B
Answer: (B) 87.5
Question: Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
(A) 2 : 3 : 4
(B) 6 : 7 : 8
(C) 6 : 8 : 9
(D) 4 : 6 : 8
(E) None of these
Rationale: Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
(140/100 * 5x), (150/100 * 7x) and (175/100* 8x)
7x, 21x/2 and 14x
The required ratio = 7x : 21x/2 : 14x
14x : 21x : 28x
2 : 3 : 4
Answer = A
Answer: (A) 2 : 3 : 4
Question: A loan shark made a loan of $100 to be repaid with $120 at the end of one month. What was the annual interest rate?
(A) 210%
(B) 220%
(C) 230%
(D) 240%
(E) None of these
Rationale: Explanation:
r=I/PT
Answer: D
Answer: (D) 240%
Question: In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of david, Benjamin, Charlene must be on the line before each of Frederick, Gale, and Harold?
(A) 1,008
(B) 1,296
(C) 2016
(D) 2,018
(E) 2,268
Rationale: Place A and E first: 8 options for D, 7 options for E.
We are left with 6 empty places. D, B and C must take first 3 places and F, G, H must take the remaining three.D, B and C can be arranged in their places in 3! ways. The same for F, G, and H.
Total = 8*7*3!*3! = 2,016.
Answer: C
Answer: (C) 2016
Question: Two squares are chosen on a chessboard at random. What is the probability that they have a side in common?
(A) 1/18
(B) 64/4032
(C) 63/64
(D) 1/9
(E) 2/9
Rationale: In 64 squares, there are:
(1) 4 at-corner squares, each has ONLY 2 squares each having a side in common with...
(2) 6*4 = 24 side squares, each has ONLY 3 squares such that each has a side in common with...
(3) 6*6 = 36 inner squares, each has 4 squares such that each has a side in common with...
So we have the calculation:
P = (4/64)*(2/63) + (24/64)*(3/63)+ (36/64)*(4/63)
P = 1/18
ANSWER:A
Answer: (A) 1/18
Question: City X has a population 5 times as great as the population of City Y, which has a population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z?
(A) 1:8
(B) 1:4
(C) 2:1
(D) 4:1
(E) 10:1
Rationale: x= 5y, y= 2*z
X : Y , Y : Z
5 : 1 , 2 : 1
10 : 2 , 2 : 1
So, X : Z = 10 : 1
(E)
Answer: (E) 10:1
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 45kg. What is the weight of the new person?
(A) 75 Kg
(B) 65 Kg
(C) 85 Kg
(D) 80 Kg
(E) 60 KG
Rationale: Explanation:
Total increase in weight = 8 Ã— 2.5 = 20
If x is the weight of the new person, total increase in weight = xâˆ’45
=> 20 = x - 45
=> x = 20 + 45 = 65
Answer: Option B
Answer: (B) 65 Kg
Question: It takes John 15 minutes to walk to the car park and 45 to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.?
(A) 8:50 a.m
(B) 8:00 a.m
(C) 7:50 a.m
(D) 6:50 a.m
(E) 9:50 a.m
Rationale: The time it takes John to get to work: time to walk to car park + time to drive
15 + 45 = 60 minutes = 1 hour
John needs to get out of the house 1 hour before 9:00 am at
9:00 - 1:00 = 8:00 a.m
correct answer B
Answer: (B) 8:00 a.m
Question: A class consists of 100 students, 25 of them are girls and 75 boys; 20 of them are rich and remaining poor; 10 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
(A) 1/200
(B) 1/59
(C) 1/56
(D) 1/54
(E) 1/53
Rationale: The probability of selecting girl is: 25/100 = 1/4
The probability of selecting rich is: 20/100 = 1/5
The probability of selecting fair complexioned is: 10/100 = 1/10
Three are independent;probability of rich and fair complexioned girl is:
(1/4) Ã—(1/5) Ã— (1/10) = 1/200
Answer: A
Answer: (A) 1/200
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
(A) 2/29
(B) 2/26
(C) 2/21
(D) 2/22
(E) 4/21
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer:C
Answer: (C) 2/21
Question: A train running at 54 kmph takes 20 seconds to pass a platform. Next it takes.12 sec to pass a man walking at 6 kmph in the same direction in which the train is going. Find the length of the train and the length of the platform
(A) 120m
(B) 125m
(C) 132m
(D) 140m
(E) 150m
Rationale: Explanation:
Let the length of train be x metres and length of platform be y metres.
Speed of the train relative to man = (54 - 6) kmph = 48 kmph
= 48×(5/18) m/sec = 40/3 m/sec.
In passing a man, the train covers its own length with relative speed.
Length of train = (Relative speed × Time) = ( 40/3)×12 m = 160 m.
Also, speed of the train = 54 ×(5/18)m / sec = 15 m / sec.
(x+y)/15 = 20 <=> x + y = 300 <=> Y = (300 - 160) m = 140 m.
Answer: Option D
Answer: (D) 140m
Question: Two trains 140 m and 200 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.9 sec
(B) 10.1 sec
(C) 10.6 sec
(D) 10.8 sec
(E) 12.24 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other
= 140 + 200 = 340 m.
Required time = 340 * 9/250
= 12.24 sec.
Answer:E
Answer: (E) 12.24 sec
Question: The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?
(A) 1000
(B) 2777
(C) 2976
(D) 2988
(E) 7122
Rationale: 2 * 22/7 * 1.75 * x = 11000
x = 1000
Answer: A
Answer: (A) 1000
Question: On the xy-plane, each point on circle C has coordinates such
that x 0 and y 0. If the center of circle C is the point (3; 12),
what is the maximum possible area of C?
(A)  6
(B)  9
(C)  24
(D)  32
(E)  64
Rationale: I think that theintentof this question is that the circle will have NO CO-ORDINATES that fit the following 2 forms: (0, Y) or (X, 0). In real basic terms, this circle will NEITHER touch (nor cross) the X-axis NOR will it touch (nor cross) the Y-axis.
With a center at (3,8), the longest possible radius would ALMOST touch the X-axis, so the radius would be a little less than 3.
If the radius WAS 3 exactly, then the area would be 9pi, which is approximately 28.26
Since the circle CAN'T touch the X-axis, the area has to be LESS than approximately 28.26
As it's written, none of the answers is clearly the correct one.
D
Answer: (D)  32
Question: The distance between two stars is 6.52 × 10^5 light years. What is the distance between the two stars in parsecs? (1 parsec = 3.26 light years)
(A) 2 × 10^5
(B) 4 × 10^6
(C) 5 × 10^7
(D) 7 × 10^7
(E) 9 × 10^8
Rationale: 6.52 × 10^5 ly / (3.26 ly/parsec) = 2 x 10^5 persec
The answer is A.
Answer: (A) 2 × 10^5
Question: The distance between two planets is 3.02 × 10^6 light years. What is the distance between the two planets, in parsecs? (1 parsec = 3.26 light years)
(A)  9.3 × 10^5
(B)  9.9 × 10^6
(C)  9.3 × 10^7
(D)  9.9 × 10^7
(E)  10.1 × 10^8
Rationale: 3.02*10^6 light years = 3.02*10^6/3.26 parsecs.
3.02/3.26 is a little bit less than 1, something like 0.9, thus 3.02*10^6/3.26 = ~0.93*10^6 = 9.3*10^5.
Answer: A.
Answer: (A)  9.3 × 10^5
Question: A boy rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately?
(A) 12.9
(B) 10.8
(C) 26.2
(D) 17.8
(E) 12.9
Rationale: Total distance traveled = 10 + 12 = 22 km /hr.
Total time taken = 10/12 + 12/10 = 61/30 hrs.
Average speed = 22 * 30/61 = 10.8 km/hr.
Answer: B
Answer: (B) 10.8
Question: What is the greatest prime factor of 4^18 - 2^28?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 127
Rationale: I'm happy to help with this.
We know 4 = 2^2, so 4^18 = (2^2)^18 = 2^(2*18) = 2^36
That takes advantage of a law of exponents that says (a^n)^m = a^(n*m)
So, 4^18 - 2^28 = 2^36 - 2^28 = 2^(28 + 8) - 2^28 = (2^28)*(2*8) - 2^28 = (2^8 - 1) *(2^28)
= (128 - 1)*(2^28) = 127*(2^28)
The prime factors of 63 are 127, so the largest prime factor is 7, answer choice D.
Here's a blog you may find helpful.
http://magoosh.com/gmat/2012/gmat-math-factors/
Does all that make sense? Please let me know if you have any further questions.
Mike
Wow. I am floored by how great of an explanation you provided. Posts like that make me really think that doing thousands of practice problems with good explanations beats out reading books on math every day of the week.
E
Answer: (E) 127
Question: In 1995, there are 28 days in February and there are 365 days in the year. In 1996, there are 29 days in February and there are 366 days in the year. If the date March 15, 1995 is a Monday, then which one of the following would the date March 15, 1996 be?
(A) Monday
(B) Tuesday
(C) Friday
(D) Wednesday
(E) Friday
Rationale: From the information given,March 15, 1996 is 366 days after March 15, 1995.
366 days = 52 weeks and 2 more days. Therefore if March 15, 1995 is a Monday, then March 15, 1996 is Monday + 2 days = Wednesday
Answer: D
Answer: (D) Wednesday
Question: 15c6+15c7+16c8=== 17cx
find x?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: 15c6=5005
15c7=6435
16c8=12870
15c6+15c7+16c8=17c9
ANSWER:D
Answer: (D) 9
Question: Find the value of X, Y by solving the below equations
X + Y = 16
X - Y = 14
(A) 16, 0
(B) 14, 2
(C) 15, 1
(D) 13, 3
(E) 11, 5
Rationale: X + Y = 16 ---(I)
X - Y = 14 -----(II) by adding (I) and (II)
------------
2X = 30 ==> X = 30/2 = 15
By Replacing the value of X in (I) we get 15 + Y = 16 ==>
Y = 16 - 15 = 1.
So, X = 15, Y = 1
Answer C) 15, 1
Answer: (C) 15, 1
Question: A man's speed with the current is 16 km / hr and the speed of the current is 2 km / hr. The man's speed against the current is
(A) 8.5 km / hr
(B) 9 km / hr
(C) 12 km / hr
(D) 12.5 km / hr
(E) None
Rationale: Sol.
Man's rate in still in water = (16 - 2) km / hr = 14 km / hr.
Man's rate against the current = (14 - 2) km / hr = 12 km / hr.
Answer C
Answer: (C) 12 km / hr
Question: If $ 5,000 is invested in an account that earns 4% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest?
(A) $ 4
(B) $ 8
(C) $ 12
(D) $ 16
(E) $ 432
Rationale: Solution
Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.04/2)^2= 5404
Amount (SI) = P+PTR/100 = 5000+(5000*1*4/100)=5400
Difference = 5404-5400=4 $
A
Answer: (A) $ 4
Question: The price of a T.V. set worth Rs. 12000 is to be paid in 20 installments of Rs. 1200 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
(A) 29997
(B) 10800
(C) 27098
(D) 19000
(E) 2799
Rationale: Money paid in cash = Rs. 1200
Balance payment = (12000 - 1200) = Rs. 10800 .Answer:B
Answer: (B) 10800
Question: If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 kmph,then the speed of the boat in still water is :
(A) 4.2 km/hr
(B) 9 km/hr
(C) 13 km/hr
(D) 21 km/hr
(E) None of these
Rationale: Solution
Rate upstream =(7/42x60)kmph = 10 kmph.
Speed of stream = 3 kmph.
Let speed in still water be x km/hr.Then, speed upstream =( x-3 ) km/hr.
∴ x - 3 = 10 or x = 13 km/hr. Answer C
Answer: (C) 13 km/hr
Question: The cost per unit of electricity during a 4 year period is as follows:
Year 1, $2 per unit;
Year 2, $3 per unit;
Year 3, $4 per unit;
Year 4, $5 per unit.
If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period?
(A) $3.82
(B) $3.62
(C) $5.12
(D) $3.12
(E) $4.12
Rationale: Let money spent each year = $60
Units bought first year = 30
Units bought second year = 20
Units bought third year = 15
Units bought fourth year = 12
Total number of units = 77
Total money spent = 60*4 = 240
Average = 240/77 = 3.12
Answer : D
Answer: (D) $3.12