mathewhe/aqua_rat huggingface dataset:
Question: The arithmetic mean of set G is zero. If H = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of G consisting of all those elements in G which are more than two but less than three standard deviations away from the arithmetic mean of G, what could be equal to the standard deviation of G?
(A) 0.54
(B) 0.77
(C) 0.82
(D) 0.97
(E) 1.62
Rationale: This is a fairly straightforward question that can be solved quickly by just applying the options
We are provided with Mean, m= 0
and H = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of S
H consists of all those elements in G that are more than 2 but less than 3 GDs away from the arithmetic mean of G
If an element is 1 GD away from the mean, we can write it as either m + GD or m - GD
Similarly, if an element is 2 GDs away from the mean, we can write it as either m + 2*GD or m - 2*GD
So, if these elements lie within 2 and 3GDs of mean, m=0
we can find which one of these values of GD satisfies each value within H
Only GD = 0.77 does
Answer : B
Answer: (B) 0.77
Question: A girl walking at the rate of 9 Km per hour crosses a square field diagonally in 12 seconds. The area of the field is:
(A) 430 Sq.m
(B) 425 Sq.m
(C) 450 Sq.m
(D) 475 Sq.m
(E) 350 Sq.m
Rationale: Distance covered in (9×1000)/(3600) × 12 = 30 m
Diagonal of squarre field = 30 m.
area of square field = 30(power)2/2
= 900/2 = 450 Sq.m
Answer is C.
Answer: (C) 450 Sq.m
Question: Of the 200 candidates who were interviewed for a position at a call center, 100 had a two-wheeler, 70 had a credit card and 140 had a mobile phone. 40 of them had both, a two-wheeler and a credit card, 30 had both, a credit card and a mobile phone and 60 had both, a two wheeler and mobile phone and 10 had all three. How many candidates had none of the three?
(A) 0
(B) 20
(C) 10
(D) 18
(E) 28
Rationale: Number of candidates who had none of the three = Total number of candidates - number of candidates who had at least one of three devices.
Total number of candidates = 200.
Number of candidates who had at least one of the three = A U B U C, where A is the set of those who have a two wheeler, B the set of those who have a credit card and C the set of those who have a mobile phone.
We know that AUBUC = A + B + C - {A n B + B n C + C n A} + A n B n C
Therefore, AUBUC = 100 + 70 + 140 - {40 + 30 + 60} + 10
Or AUBUC = 190.
As 190 candidates who attended the interview had at least one of the three gadgets, 200 - 190 = 10 candidates had none of three.
ANSWER:C
Answer: (C) 10
Question: The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.8. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?
(A) 1/5
(B) 2/5
(C) 3/5
(D) 4/5
(E) 12/25
Rationale: p(m) =0.2
p(r) =0.2
p(m intersection r) = 0 (If events M and R cannot both occur)
p(m or r) = 0.2+0.2 =0.4
Corrected !!
Answer B
Answer: (B) 2/5
Question: Simplify: (i) 12.05*5.4+0.6
(A) 101.45
(B) 103.45
(C) 108.45
(D) 107.45
(E) 109.45
Rationale: Given exp. = 12.05*(5.4/0.6) = (12.05*9) = 108.45
Answer is C.
Answer: (C) 108.45
Question: How many different ways can 2 students be seated in a row of 6 desks, so that there is always at least one empty desk between the students?
(A)  2
(B)  3
(C)  4
(D) 20
(E)  12
Rationale: 10 ways to seat the students:
with two empty seats between
1 empty w/ one student on the left most
1 empty....right most
two students can be interchanged
10x2=20
D
Answer: (D) 20
Question: If a 3-member subcommittee is to be formed from a certain 5-member committee, how many different such subcommittee are possible?
(A) 6
(B) 10
(C) 20
(D) 108
(E) 216
Rationale: 1st member can be selected in 5 ways
2nd can be selected in 4 ways
3rd can be selected in 3 ways
So total ways : 60
But to avoid the similar scenarios 60/3!=10
ANS:B
Answer: (B) 10
Question: A train 400 m long passed a pole in 40 sec. How long will it take to pass a platform 600 m long?
(A) 28 sec
(B) 100 sec
(C) 85 sec
(D) 16 sec
(E) 15 sec
Rationale: Speed = 400/40 = 10 m/sec.
Required time = (400 + 600)/10
= 100 sec.
Answer:B
Answer: (B) 100 sec
Question: In a certain parking lot, 2% of the cars are towed for parking illegally. However 90% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally?
(A) 10%
(B) 12%
(C) 16%
(D) 18%
(E) 20%
Rationale: Let x be the number of cars and let y be the number of cars parked illegally.
2%*x = 10%*y
y/x = 1/5 = 20%
The answer is E.
Answer: (E) 20%
Question: A bulldog received 1,600 votes in a bulldog competition, giving him 20 percent of the votes. What percent of the remaining votes would he have needed to receive in order to win 34 percent of the total votes?
(A) 10%
(B) 12.5%
(C) 15%
(D) 17.5%
(E) 20%
Rationale: There were 80% of the votes remaining and he needed 14%/80% = 7/40 = 17.5%
The answer is D.
Answer: (D) 17.5%
Question: There is a sequence ni such, in which i is a positive integer, ni+1=2ni.
If n1=1, n2=2, n3=4, n4=8, what is the scope including n51?
(A) 100~1,000
(B) 1,000~10,000
(C) 10,000~100,000
(D) 100,000~1,000,000
(E) 1,000,000,000,000,000~
Rationale: -> ni=2^(i-1) -> 2^10=1,024>1,000=10^3 -> n51=2^50=(2^10)^5>(10^3)^5=10^15
Thus, the answer is E.
Answer: (E) 1,000,000,000,000,000~
Question: An outlet pipe can empty 2/3 of a cistern in 16 minutes. In 4 minutes, what part of the cistern will be emptied?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/6
(E) 1/8
Rationale: 4/16 * 2/3 = 1/6
The answer is D.
Answer: (D) 1/6
Question: In a friendship gang Andrew has 8 gang, in how many ways can he invite one ormore of the gang to his house?
(A) 234
(B) 255
(C) 260
(D) 265
(E) 278
Rationale: Andrew can select one or more than one of his 8 gang.
=> Required number of ways = 28 – 1= 255.
B
Answer: (B) 255
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 8
(B) 7
(C) 6
(D) 5
(E) 2
Rationale: 80% --- 12
120% --- ?
80/120 * 12 = 8
Answer: A
Answer: (A) 8
Question: 4, 6, 12, 14, 28, 30, ?
(A) 20
(B) 40
(C) no=60
(D) 80
(E) 100
Rationale: C
60
The given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The pattern is +8, +16, +32. So, the missing number = (28 + 32) = 60
Answer: (C) no=60
Question: At present, the ratio between the ages of Arun and Deepak is 4:2. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
(A) 10 years
(B) 15 years
(C) 18 years
(D) 12 years
(E) 19 years
Rationale: Let the present ages of Arun and Deepak be 4x and 2x years respectively.
Then, 4x + 6 = 26 => x
= 5
Deepak's age
= 2x
= 10 years.
Answer:A
Answer: (A) 10 years
Question: The remainder when A=1+3+3^2+3^3+..........+3^200 is divided 13.
(A) 12
(B) 7
(C) 0
(D) 5
(E) 3
Rationale: A=1+3+3^2+3^3+..................+3^200
Is a Geometric progression having common ratio as '3' and number of terms as '201'.
Since Sum to n terms in GP = a(r^n-1)/(r-1)
where a=First term and r =common ration
Hence,
1*(3^201 -1 )/(3-1)
Rem of (3^201-1)/2 divided by 13
3^201 -1 /26
WKT, 3^3 = 27 = 26+1
{(26+1)^67 - 1}/26
{1-1}/26
=>0.C
Answer: (C) 0
Question: On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 80% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?
(A)  36%
(B)  60%
(C)  66%
(D)  80%
(E)  84%
Rationale: Chris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.8*0.8 = 0.64. So, the probability that he will be able to attend is 1 - 0.64 = 0.36.
Answer: A.
Answer: (A)  36%
Question: If the sum of a number and its square is 132, what is the number?
(A) 15
(B) 11
(C) 28
(D) 91
(E) none of these
Rationale: Let the number be x. Then,
x + x2 = 132
(x + 12)(x - 11) = 0
x = 11
ANSWER:B
Answer: (B) 11
Question: If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability K that a number picked up in first 90 positive integers will have the result of # as an odd digit ?
(A) (a) 4/10
(B) (b) 4/9
(C) (c) 1/2
(D) (d) 6/10
(E) (e) 5/9
Rationale: Here is how I did it. Probably there may be better way to do it.
First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90.
That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment.
So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17)
Number of integers, whose digits add to 1: 1 and 10 = 2
Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4
Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6
Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8
Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10
Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8
Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6
Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4
Number of integers, whose digits add to 16: 79, 88 = 2
So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers
Probability K= 50/90 = 5/9
Correct answer E
Answer: (E) (e) 5/9
Question: Marcella has 26 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left?
(A) 21
(B) 20
(C) 19
(D) 16
(E) 15
Rationale: Marcella has 26 pairs of shoes and loses 9 shoes.
To minimize the loss of identical pairs of shoes we want Marcella to lose as many identical pairs as possible. This would yield 4 identical pairs and 1 additional shoe (destroying 5 pairs of shoes).
The 26 pairs of shoes minus the 5 'destroyed' pairs yields 21 pairs that still fulfill the requirements.
Answer: A
Answer: (A) 21
Question: Every day Daniel drives 60 miles back from work. On Sunday, Daniel drove all the way back from work at a constant speed of x miles per hour. On Monday, Daniel drove the first 32 miles back from work at (2x) miles per hour, and the rest of the way at (x/2) miles per hour. The time it took Daniel to drive back from work on Monday is longer than the time it took him to drive back from work on Sunday by what percent?
(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 50%
Rationale: Let's TEST X = 4....
On Sunday, Daniel drove 60 miles at 4 miles/hour.
D = (R)(T)
60 = (4)(T)
60/4 = 15 = T
It takes 15 hours to drive home
On Monday, Daniel drove the first 32 miles at (2)(4) = 8 miles/hour and the rest of the way (28 miles) at 4/2 = 2 miles/hour
D = (R)(T)
32 = (8)(T)
32/8 = 4 = T
It takes 4 hours for the first part
D = (R)(T)
28 = (2)(T)
28/2 = 14 = T
It takes 14 hours for the second part
Total time to drive home on Monday = 4+14 = 18 hours
We're asked by what percent 18 hours is greater than 15 hours.
18/15 = 1.2, so it is 20% greater.
B
Answer: (B) 20%
Question: There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 65% play football, how many play both?
(A) 120
(B) 150
(C) 240
(D) 180
(E) 160
Rationale: n(A) = 75*600/100 = 450
n(B) = 65*600/100 = 390
n(AUB) = 600
n(AnB) = 450+390-600 = 240
Answer is C
Answer: (C) 240
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6800?
(A) s. 4991
(B) s. 5991
(C) s. 6001
(D) s. 6791
(E) s. 7991
Rationale: total fr 5 mnths=(6435+6927+6855+7230+6562)=Rs34009.
Reqd.sale=Rs.[(6800*6)-34009]
= Rs.(40800-34009)
= Rs.6791.
ANSWER:D
Answer: (D) s. 6791
Question: Which of the following fractions has a decimal equivalent that is a terminating decimal?
(A) 10/189
(B) 15/196
(C) 16/225
(D) 25/144
(E) 39/128
Rationale: a) 10/189
denominator sum of digits is 18 so its divisible by 3 eliminate
b) 15/196
This has a prime factor of 7 when do the prime factorization of the denominator.. Eliminate
c) 16/225
denominator sum of digits is 9 so its divisible by 3 eliminate
d) 25/144
denominator sum of digits is 9 so its divisible by 3 eliminate
e) 39/128 Correct answer
ANSWER:E
Answer: (E) 39/128
Question: Sophia finished 2/3 of a book. She calculated that she finished 30 more pages than she has yet to read. How long is her book?
(A) A)90
(B) B)150
(C) C)130
(D) D)190
(E) E)210
Rationale: Let x be the total number of pages in the book, then she finished 2/3*x pages.
Then she has x−2/3*x=1/3*x pages left.
2/3*x−1/3*x=30
1/3*x=30
x=90
So the book is 90 pages long.
Answer is A.
Answer: (A) A)90
Question: A train 510 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40
(B) 52
(C) 26
(D) 21
(E) 14
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 510 + 140 = 650 m
Required time = 650 * 2/25 = 52 sec
Answer:B
Answer: (B) 52
Question: What is the next number of the following sequence
12, 36, 80, 150,.... ?
(A) 252
(B) 262
(C) 272
(D) 282
(E) 292
Rationale: 12=2^3+2^2
36=3^3+3^2
80=4^3+4^2
150=5^3+5^2
=>6^3+6^2=216+36=252
ANSWER:A
Answer: (A) 252
Question: What is the sum of the greatest common factor and the lowest common multiple of 36 and 56?
(A) 512
(B) 508
(C) 451
(D) 516
(E) 451
Rationale: Prime factorization of 36 = 2 x 2 x 3 x 3
Prime factorization of 56 = 2 x 2 x 2 x 7
GCF = 4
LCM = 504
Sum = 508
Ans: B
Answer: (B) 508
Question: Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:
(A) 40
(B) 80
(C) 120
(D) 200
(E) 130
Rationale: Explanation:
Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or x = 40.
The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40. Answer: A
Answer: (A) 40
Question: Which greatest possible length can be used to measure exactly 15 meter 75 cm, 11 meter 25 cm and 7
meter 65 cm
(A) 45cm
(B) 255cm
(C) 244cm
(D) 55cm
(E) None of these
Rationale: Explanation:
Convert first all terms into cm.
i.e. 1575 cm, 1125cm, 765cm.
Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms
is 255.
Answer: Option A
Answer: (A) 45cm
Question: The average of 2,7,6 and x is 5 and the average of 18,1,6,x and y is 10. What is the value of y?
(A) 10
(B) 20
(C) 15
(D) 25
(E) 30
Rationale: We have : (2+7+6+x) /4 = 5
15+x = 20
x = 5
(18+1+6+x+y)/5 = 10
25+5+y = 50
y = 20
Answer is B
Answer: (B) 20
Question: The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. what is the age of the youngest child ?
(A) 4
(B) 8
(C) 10
(D) None of these
(E) Cannot be determined
Rationale: Explanation:
Let x = the youngest child. Each of the other four children will then be x+3, x+6, x+9, x+12.
We know that the sum of their ages is 50 .
so, x+(x+3)+(x+6)+(x+9)+(x+12) = 50
inline Rightarrow x= 4
inline therefore The youngest child is 4 years old. Answer: C
Answer: (C) 10
Question: A can do work in 9 days, B can do work in 18 days. In how many days they will complete the work together.
(A) 8 days
(B) 7 days
(C) 6 days
(D) 5 days
(E) 4 days
Rationale: Bigger no=18, Ratio=9:18=1:2
No of days = 18/(1 + 2)
= 6 days
ANSWER:C
Answer: (C) 6 days
Question: The largest five digit number which is a perfect cube, is:
(A) 85184
(B) 91125
(C) 97336
(D) 96806
(E) 99999
Rationale: Explanation:
46*46*46 = 97336
Answer: C
Answer: (C) 97336
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?
(A) 150 meter
(B) 170 meter
(C) 156 meter
(D) 168 meter
(E) 154 meter
Rationale: Speed = 60*(5/18) m/sec
= 50/3 m/sec
Length of Train (Distance)
= Speed * Time
(50/3) * 9
= 150 meter
Answer:A
Answer: (A) 150 meter
Question: If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 11% per annum then the gain of B in a period of 3 years is?
(A) 110
(B) 106
(C) 105
(D) 107
(E) 109
Rationale: (3500*1*3)/100 => 105
Answer: C
Answer: (C) 105
Question: In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (12, 0), (0, -3.5), (-12, 0)?
(A) 84
(B) 88
(C) 112
(D) 116
(E) 120
Rationale: Area of rhombus= 1/2* D1 *D2
Length of 1st diagonal = 12+12= 24
Length of 2nd diagonal= 3.5+3.5= 7
Area= 1/2*24*7= 84
A is the answer
Answer: (A) 84
Question: In an election, candidate Smith won 52% of the total vote in Counties A and D. He won 61% of the vote in County A. If the ratio of people who voted in County A to County D is 3:1, what percent of the vote did candidate Smith win in County D ?
(A) A.25%
(B) B.27%
(C) C.34%
(D) D.43%
(E) E.49%
Rationale: (61%)*3x + (y%)*x = (52%)*4x
y = 25% of County D
hence answer is A.
Answer: (A) A.25%
Question: Two pipes can fill a tank in 24 min and 32 min respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min ?
(A) 4 min
(B) 6 min
(C) 9 min
(D) 8 min
(E) 12 min
Rationale: Pipe A will run for 18 minutes
Sp pipe A will do = 18/24 = 3/4 portion of the work
left work is 1/ 4
Just assume that what will be 1/4 if multiplied with 1/32 (B's rate )
Only 8 will make it 1/4
So after 8 minutes B should be stopped
Answer : D
Answer: (D) 8 min
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
(A) 14 years
(B) 19 years
(C) 24 years
(D) 33 years
(E) 38 years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
Answer: Option A
Answer: (A) 14 years
Question: How many seconds will a 700 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 23 sec
(B) 30 sec
(C) 27 sec
(D) 36 sec
(E) 42 sec
Rationale: Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18
= 50/3 m/sec.
Time taken to pass the man = 700 * 3/50
= 42 sec.
Answer:E
Answer: (E) 42 sec
Question: A local restaurant recently renovated its dining space, purchasing new tables and chairs to use in addition to the original tables and chairs. The new tables each seat six customers, while the original tables each seat four customers. Altogether, the restaurant now has 40 tables and is capable of seating 212 customers. How many more new tables than original tables does the restaurant have?
(A) 8
(B) 12
(C) 20
(D) 24
(E) 28
Rationale: If all the tables seated 4, the number of customers could be 4*40 = 160.
212-160 = 52, so 52/2 = 26 tables must be tables seating 6 people.
The number of tables seating 4 people is 40-26 = 14.
The number of new tables is 26-14 = 12 more than the number of old tables.
The answer is B.
Answer: (B) 12
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
(A) 176 Sec
(B) 190 Sec
(C) 178 Sec
(D) 267 Sec
(E) 276 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer:B
Answer: (B) 190 Sec
Question: One filter decreases the concentration of harmful substances in water by half. If water that contains less than 0.1 percent of harmful substances is considered clean, how many filters are required to clean 200 liters of water containing 0.5 liters of harmful substances ?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: Initially, the concentration of harmful substances in the water is 0.5/200∗100%=0.25%. One filter will reduce this concentration to 0.125%. Two filters will reduce the concentration to 0.0625% which is less than 0.1%
Answer: A
Answer: (A) 2
Question: The function f is defined for all positive integers m by the following rule. f(m) is the number of positive integers each of which is less than m and has no positive factor in common with m other than 1. If p is any prime, number then f(p)=
(A) p-1
(B) p-2
(C) (p+1)/2
(D) (p-1)/2
(E) 2
Rationale: If not the wording the question wouldn't be as tough as it is now. The GMAT often hides some simple concept in complicated way of delivering it.
This question for instance basically asks: how many positive integers are less than given prime number p which have no common factor with p except 1.
Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).
For example: if p=8 how many numbers are less than 8 having no common factors with 8: 1, 2, 3, 4, 5, 6, 7 --> 8-1=7.
Answer: A.
Answer: (A) p-1
Question: If X is 30% greater than Y, Z is 25% smaller than how much percent is X greater than Z?
(A) 25%
(B) 73 1/3%
(C) 73%
(D) 74%
(E) None of these
Rationale: Explanation:
X = 130
Y = 100
Z = 75
X-Z/Z * 100 = 55/75 * 100 = 5500/75 % = 73 1/3% greater than Z
Answer: Option B
Answer: (B) 73 1/3%
Question: What is the smallest integer w greater than 1 that leaves a remainder of 1 when divided by any of the integers 6, 8, and 10?
(A) 21
(B) 41
(C) w=121
(D) 241
(E) 481
Rationale: Or u can just use the answer choices here. Since the answers are already arranged in ascending order, the first number which gives remainder w as 1 for all three is the correct answer. In the given question, the first number which gives a remainder of 1 for 6,8 and 10 is 121.C
Answer: (C) w=121
Question: Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together?
(A) 17 1/7
(B) 17 1/5
(C) 17 1/8
(D) 17 1/1
(E) 17 1/2
Rationale: 1/30 + 1/40 = 7/120
120/7 = 17 1/7 days
Answer: A
Answer: (A) 17 1/7
Question: If 0 < x < 7 and 0 < y < 9, then the lowest possible value for xy is
(A) between 60 and 70
(B) between 0 and 60
(C) 0
(D) between 0 and -70
(E) less than -70
Rationale: If 0 < x < 7 and 0 < y < 9, then the lowest possible value for xy is
A. between 60 and 70
B. between 0 and 60
C. 0
D. between 0 and -70
E. less than -70
Say y = 8 (y<9)
x = 6
So xy =48 which is less than 60.
Answer is B
Answer: (B) between 0 and 60
Question: A taxi company charges $1.15 for the first quarter of a mile and fifteen cents for each additional quarter of a mile. What is the maximum distance someone could travel with $4.90?
(A) 4 miles
(B) 4 1/4 miles
(C) 4 3/4 miles
(D) 5 1/2 miles
(E) 6 1/2 miles
Rationale: If we start out with $4.90 and have to spend $1.15 for the first quarter-mile, we will have $3.75 left to spend on quarter-mile intervals.
Since $3.75/$0.15 = 25, we can buy 25 more quarter-miles, and will travel 26 quarter miles in all:
26 × 1/4 = 6 1/2 miles.
The correct answer is choice (E).
Answer: (E) 6 1/2 miles
Question: A certain essay consists of 15 paragraphs. Each paragraph contains at least 130 words but not more than 140 words. Which of the following could be the total number of words in the essay?
(A) 1440
(B) 1540
(C) 1640
(D) 1740
(E) 2050
Rationale: lets consider minimum no of words ... 15 * 130 = 1950
Lets consider maximum no of words .... 15*140= 2100
answer should be one of these two values or should lie between these two values ...
only 1 option E - 2050
Answer: (E) 2050
Question: A school has received 60% of the amount it needs for a new building by receiving a donation of $400 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?
(A) $200
(B) $177.78
(C) $100
(D) $277.78
(E) $377.78
Rationale: Let us suppose there are 100 people. 40% of them donated $16000 ( 400 * 40 )
$16000 is 60% of total amount.
So total amount = 16000 * 100/60
Remaining amount is 40% of total amount.
40% of total amount = 16000 * (100/60) * (40/100) = 32000/3
This amount has to be divided by 60 ( remaining people are 60 )
So per head amount is 32000/3 / 60 = 32000/180 = 1600/9 = $177.78;
ANSWER:B
Answer: (B) $177.78