mathewhe/aqua_rat huggingface dataset:
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
(A) 7
(B) 8
(C) 6
(D) 4
(E) 2
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer: B
Answer: (B) 8
Question: Two trains each 475 m long are running in opposite directions on parallel tracks. Their speeds are 55 km/hr and 40 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 77 sec
(B) 66 sec
(C) 48 sec
(D) 36 sec
(E) 45 sec
Rationale: Relative speed = 55+40 = 95 km/hr.
95 * 5/18 = 475/18 m/sec.
Distance covered = 475 + 475 = 950 m.
Required time = 950 * 18/475 = 36 sec.
Answer: D
Answer: (D) 36 sec
Question: Present ages of Sameer and Anand are in the ratio of
5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
(A) 24
(B) 27
(C) 40
(D) cannot be determined
(E) None
Rationale: Solution
Let the present ages of sameer and anand be 5x years and 4x years respectively.
Then	5x+3/4x+3=11/9
≈9(5x+3)=11(4x+3)
x=6.
Anands's present age	= 4x
=24 years.
Answer A
Answer: (A) 24
Question: If 15 toys cost Rs, 234, what do 35 toys cost?
(A) Rs.546
(B) Rs.754
(C) Rs.590
(D) Rs.520
(E) Rs.600
Rationale: . Let the required cost be Rs. x. Then,
More toys, More cost	(Direct Proportion)
.	15 : 35 : : 234 : x  (15 x x) = (35 x 234)  x=(35 X 234)/15 =546
Hence, the cost of 35 toys is Rs. 546.
Answer is A
Answer: (A) Rs.546
Question: A number increased by 40% gives 700. The number is
(A) 250
(B) 500
(C) 450
(D) 500
(E) 520
Rationale: Formula = TOTAL=100% ,INCRESE = "+" DECREASE= "-"
A number means = 100 %
That same number increased by 40 % = 140 %
140 % ------->700 (140× 5 = 700)
100 % -------> 700 (100 × 5 = 500)
B)
Answer: (B) 500
Question: A train crosses a platform of 110 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 150
(B) 88
(C) 77
(D) 310
(E) 52
Rationale: Length of the train be â€˜Xâ€™
X + 110/15 = X + 250/20
4X + 440 = 3X + 750
X = 310m
Answer: D
Answer: (D) 310
Question: The smallest 3 digit prime number is:
(A) 103
(B) 106
(C) 107
(D) 112
(E) 101
Rationale: A
103
The smallest 3-digit number is 100, which is divisible by 2.
100 is not a prime number.
√101< 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.
101 is a prime number.
Hence 101 is the smallest 3-digit prime number.
Answer: (A) 103
Question: Walking at 5/6 of its usual speed, a train is 10 minutes too late. What is usual time to cover the journey?
(A) 70 minutes
(B) 2 hours
(C) 2/3 hours
(D) 5/6 hours
(E) 85 minutes
Rationale: et Speed be S and Time to cover the journey be T
S * T = D (distance of journey) --- 1
now as per the question stem we have
(5/6)S * (T + 10) = D ----2
Equating Value of D from (1) in (2) we get T = 50mins or 5/6hrs .
Answer: D
Answer: (D) 5/6 hours
Question: The difference between the heights of two trees is 20 cm. Ten years ago, the taller one was thrice as taller as the shorter one. The present height of the taller tree is
(A) 300cm
(B) 15cm
(C) 20cm
(D) 10cm
(E) 40cm
Rationale: Let their heights of x cm and (x + 20) cm respectively.
Then, (x + 20) - 10 = 3(x - 10)
⇔ x +10= 3x - 30
⇔ 2x = 40
∴ Present height of taller tree = (20 + 10)
= 30cm.
Answer :30cm
Answer: (A) 300cm
Question: The set X consists of the following terms: {4,44,444,4444,.....}, where the nth term has n 4's in it for example 10th term is 4444444444. What is the hundreds digit of the sum of the first 75 terms of set X?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: 75*4 + 74*40 + 73*400 = 300 + 2960 + 29200 = 32460
The hundreds digit is 4.
The answer is C.
Answer: (C) 4
Question: A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
(A) 5kmph
(B) 7kmph
(C) 6kmph
(D) 4kmph
(E) 4.5kmph
Rationale: Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr.
30/(15+x) + 30/(15-x) = 4.5
9 * x^2 = 225
x^2 = 25
x = 5 kmph
Ans- A
Answer: (A) 5kmph
Question: A searchlight on top of the watch-tower makes 3 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 15 seconds?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4
Rationale: 3 revolutions per minute = 1 revolution every 20 seconds
So no matter what anybody appearing at the tower cannot stay in the dark for more than 20 seconds. This will be our total number of possibilities i.e the denominator.
P(man in dark for at least 15 seconds) = 1 - P (man in dark for max of 15 seconds) = 1 - 15/20 = 1 - 3/4 = 1/4
or the other way would be:
P(man in dark for at least 5 seconds) is like saying he can be in dark for 5,6,7...all the way to 20 seconds because that is the max. In this approach it would be 5/20 seconds = 1/4.
Answer is A
Answer: (A) 1/4
Question: A ship went on a voyage after 180 miles a plane statrted with 10 times speed that of the ship.Find the distance when they meet from starting point.
(A) 200 miles
(B) 179 miles
(C) 146 miles
(D) 149 miles
(E) 143 miles
Rationale: Let the distance traveled by the ship after 180 miles to meet the plane be 'd'
Speed of the ship be 'x' and speed of the ship be '10x'
Time taken by plane to travel 180+d dist. = time take by ship for 'd' dist.
(180+d)/10x=d/x
180+d=10d
d=180/9=20.
So the distance traveled when they meet from starting point=180+d=200 miles
ANSWER:A
Answer: (A) 200 miles
Question: A polygon has 230 diagonals. How many sides does it have?
Self made
(A)  22
(B)  23
(C)  24
(D)  25
(E)  26
Rationale: The best way to solve this problem is to use the formula: An n sided polygon can have n*(n - 3)/2 diagonals
n*(n - 3)/2 = 230
n*(n - 3) = 460
Substitute n from the answer choices. n = 23
Answer: B
Answer: (B)  23
Question: If x : y = 1 : 3, find the value of (2x + 3y) : (5x – y)
(A) 11:3
(B) 11:2
(C) 3:2
(D) 7:2
(E) 9:5
Rationale: Explanation:
Given: x/y = 1/3
(2x + 3y)/(3x – y)
= (2*1 + 3*3) : (5*1 – 3)
= 11:2
ANSWER: B
Answer: (B) 11:2
Question: Stacy and Helon are 30 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 1 mile per hour faster than helon's constant rate of 5 miles/hour. If Helon starts her journey 24 minutes after Stacy, how far from the original destination has Helon walked when the two meet?
(A) 5 miles
(B) 8 miles
(C) 6 miles
(D) 13 miles
(E) 12 miles
Rationale: Original distance between S and H = 30 miles.
Speed of S = 5+1 = 6 mph, Speed of H = 5 mph.
Time traveled by H = t hours ---> time traveled by S = t+24/60 = t+2/5 hours.
Now, the total distances traveled by S and H = 20 miles ---> 6*(t+2/5)+5*t=30 ---> t= 138/55 hours. Thus H has traveled for 138/55 hours giving you a total distance for H = 5*138/55 = 13 miles.
D is thus the correct answer.
P.S.: based on the wording of the question, you should calculatehow far from theoriginal destination has Heather walkedwhen the two meet. 'Original destination' for H does not make any sense. Original destination for H was situated at a distance of 20 miles.
Answer: (D) 13 miles
Question: 9873 + x = 13200, then x is ?
(A) 3327
(B) 3237
(C) 3337
(D) 2337
(E) None of these
Rationale: Answer
x = 13200 - 9873 = 3327
Option: A
Answer: (A) 3327
Question: A train is moving at a speed of 132 km/hr. If the length of the train is 100 meters, how long will it take to cross a railway platform 230 meters long
(A) 6 ½ sec
(B) 7 ½ sec
(C) 8 sec
(D) 8 ½ sec
(E) 9 sec
Rationale: Explanation:
Speed of train = 132 ×(5/18) m/sec = 110/3 m/sec.
Distance covered in passing the platform = (100 + 230) m = 330 m.
Time taken =330×(3/110) sec = 9 sec
Answer: Option E
Answer: (E) 9 sec
Question: How long does a train 100 m long running at the speed of 75 km/hr takes to cross a bridge 135 m length?
(A) 11.3 sec
(B) 12.1 sec
(C) 13.1 sec
(D) 16.5 sec
(E) 12.7 sec
Rationale: Speed = 75 * 5/18
= 20.8 m/sec
Total distance covered
= 100 + 135 = 235 m.
Required time = 235/20.8 '
= 11.3 sec.
Answer:A
Answer: (A) 11.3 sec
Question: A side of beef lost 35 percent of its weight in processing. If the side of beef weighed 546 pounds after processing, how many pounds did it weigh before processing?
(A) 191
(B) 355
(C) 737
(D) 840
(E) 1,560
Rationale: Let weight of side of beef before processing = x
(65/100)*x = 546
=> x = (546 * 100)/65 = 840
Answer D
Answer: (D) 840
Question: Let p be a prime number. If N = 7P, how many divisors does N have?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Two. N = 7*p, and both 7 and p are prime. So the answer is B.
Answer: (B) 2
Question: Suraj has a certain average of runs for 8 innings. In the 9th innings he scores 90 runs thereby increasing his average by 6 runs. What is his average after the 9th innings?
(A) 42
(B) 64
(C) 36
(D) 72
(E) 27
Rationale: To improve his average by 6 runs per innings he has to contribute 8 x 6 = 48 runs for the previous 8 innings.
Thus, the average after the 9th innings
= 90 - 48 = 42.
ANSWER:A
Answer: (A) 42
Question: If the shirt is selling for $150 and C.P is 30% of S.P. Then what is the profit percent
(A) 130%
(B) 150%
(C) 160%
(D) 170%
(E) 180%
Rationale: Explanation:
Let the S.P = 150
then C.P. = (40/100)*150 = 60
Profit = 90
Profit% = (90/60) * 100 = 150%. Answer: B
Answer: (B) 150%
Question: The radius of a cylindrical vessel is 7cm and height is 4cm. Find the whole surface of the cylinder?
(A) 484
(B) 771
(C) 440
(D) 767
(E) 1981
Rationale: r = 7 h = 4
2πr(h + r) = 2 * 22/7 * 7(11) = 484
Answer:A
Answer: (A) 484
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is
(A) 6 days
(B) 7 days
(C) 8 days
(D) 9 days
(E) 11 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 × 40/50 = 8 days.
C
Answer: (C) 8 days
Question: A school’s annual budget for the purchase of student computers increased by 70% this year over last year. If the price of student computers increased by 30% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?
(A) 30%
(B) 30.77%
(C) 36%
(D) 37%
(E) 38%
Rationale: Pick numbers.
Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1 = 100;
This year: budget = $170, price = $1.3 --> the number of computers purchased = 170/1.3 = ~130.77
Increase in the number of computers purchased = 30.77%.
Answer: B.
Answer: (B) 30.77%
Question: If 292,102 football shoes need to be placed in boxes and each box can contain at most 13 pair of football shoes. How many pair of football shoes will be in the last unfilled box?
Options:
(A) 1football shoes
(B) 6 football shoes
(C) 4 football shoes
(D) 7 football shoes
(E) 9 football shoes
Rationale: The number of football shoes that can be placed in boxes of 13 football shoes is the first number that is divisible by 13 that occurs before 292,102.
In order to divide the sum in 13 parts, the amount must be divisible by 13
Divisibility rule of 13: The sum of the digits must be divisible by 13
Add four times the last digit to the remaining leading truncated number.
292,102->29210+8=29218->2921+32=2953->295+12=307->30+28=58
Hence, we need to remove 6 to this number for it to be divisible by 13
Correct Option: B
Answer: (B) 6 football shoes
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 100
(B) 120
(C) 130
(D) 150
(E) 160
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.
Answer: Option D
Answer: (D) 150
Question: How many different sections of 4 books can be made from 10 different books if two books are always selected.
(A) 48
(B) 18
(C) 38
(D) 28
(E) 35
Rationale: If two particular books are always selected. This means two books are selected out of the remaining 8 books. Required number of ways =8C2 =8!/2!6! =28. Answer : D
Answer: (D) 28
Question: 75 boys can complete a work in 36 days.how many men need to complete twice the work in 20 days
(A) 160
(B) 170
(C) 270
(D) 190
(E) 200
Rationale: one man can complete the work in 36*75=2700 days = one time work
to Complete the work twice it will be completed in
let M be the no. of worker assign for this therefore the eqn becomes
M*20=2*2700
M=270 workers
ANSWER:C
Answer: (C) 270
Question: Elena’s bread recipe calls for 3 ounces of butter for each 4 cups of flour used. She needs to make 7 times the original recipe. If 12 ounces of butter is used, then how many cups of flour are needed?
(A) 1
(B) 4
(C) 9
(D) 13
(E) 28
Rationale: Solving through algebra route:
3B + 4F = x amount
If we multiply this equation with 7 we get:
21B + 28F =7X
Therefore, we got 21 ounces of butter and 7X amount of quantity when we use 28 ounces of floor.
Ans:E
Answer: (E) 28
Question: In a 120-mile trip, the first 40 miles were completed at 60 mph. If the average speed for the whole trip was 50 mph, what was the average speed in the last 80 miles?
(A) 585/13 mph
(B) 590/13 mph
(C) 595/13 mph
(D) 600/13 mph
(E) 605/13 mph
Rationale: The time to complete the first 40 miles was (40 miles / 60 mph) = (2/3) hours.
The time to complete the whole trip was (120 miles / 50 mph) = (12/5) hours.
The time to complete the last 80 miles was (12/5) - (2/3) = (26/15) hours.
The average speed in the last 80 miles was (80 miles / (26/15) hours) = 600/13 mph.
The answer is D.
Answer: (D) 600/13 mph
Question: If set A={3,3,3,....,n times} , set B={3,3,3,3....m times} and set C={11,11,11...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ?
(A) a) k(n+m+mn)+ k
(B) b) (1+n+m+mn)(k+1)
(C) c) k^2(mn+n/m)
(D) d) kmn(k+m+n)
(E) e) None of the above.
Rationale: a) how many 2's are included?
b) how many 3's are included?
and
c) how many 11's are included?
For the number of 2, we could have zero 2's, or one 2, or two 2's, all the way up to n 2's. That's (n + 1) possibilities for the 2's. Similarly, (m + 1) possibilities for the 3's and (k + 1) possibilities for the 11's. We simply multiply these three numbers.
NOTICE that one set, the set that includes no 2's, no 3's, and no 11's, is included. This is known in mathematics as thenull set, sometimes called the empty set, a set with no members. Technically, this is a subset of every possible set, but that's a technical detail of set theory that goes well beyond what the GMAT would expect students to know. Even the the calculation is not that difficult, some of the technical aspects of this question are not in line with the GMAT's expectations.
The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together:
(mn + m + n + 1)(k + 1).
Mike
D
Answer: (D) d) kmn(k+m+n)
Question: If A and B are two prime numbers bigger than 2, which of the following can't be true?
(1) A + B is an even number.
(2) A - B is also a Even number.
(3) A^B is also a prime number.
(A) 1 only.
(B) 2 only.
(C) 3 only.
(D) 2 and 3 only.
(E) 1, 2 and 3.
Rationale: Answer is D : 2 and 3 only
(1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true
(2) A - B is also a Even number. : True
(3) A^B is also a prime number. : Beats the property of primes, so false
Ans : C
Answer: (C) 3 only.
Question: There are 24 students in a seventh grade class. They decided to plant birches and roses at the school's backyard. While each girl planted 3 roses, every three boys planted 1 birch. By the end of the day they planted 2424 plants. How many birches and roses were planted?
(A) 6
(B) 7
(C) 8
(D) 2
(E) 9
Rationale: Let xx be the number of roses. Then the number of birches is 24−x24−x, and the number of boys is 3×(24−x)3×(24−x). If each girl planted 3 roses, there are x3x3 girls in the class.
We know that there are 24 students in the class. Therefore x3+3(24−x)=24x3+3(24−x)=24
x+9(24−x)=3⋅24x+9(24−x)=3⋅24
x+216−9x=72x+216−9x=72
216−72=8x216−72=8x
1448=x1448=x
x=18x=18
So, students planted 18 roses and 24 - x = 24 - 18 = 6 birches.
Answer:A
Answer: (A) 6
Question: A train ride from Two P to Town Q costs $6.85 more than does a bus ride from Town P to Town Q. Together, the cost of one train ride and one bus ride is $9.85. What is the cost of a bus ride from Town P to Town Q?
(A) $1.50
(B) $2.50
(C) $4.10
(D) $4.70
(E) $8.20
Rationale: Let x be the cost of a bus ride.
x + (x+685) = 985
2x = 300
x = $1.50
The answer is A.
Answer: (A) $1.50
Question: A fruit salad mixture consists of apples, peaches, and grapes. There are 3 times as many pounds of apples as grapes and 2.5 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 39 pounds per fruit, how many more pounds of apples than grapes does the mixture have?
(A) 5
(B) 12
(C) 19
(D) 36
(E) 50
Rationale: A+P+G= 39*3
A=3G
P=2.5G
3G+2.5G+G= 39*3
G=39*3/6.5= 18
A= 6*3=54
Difference = 36
'D' is the answer
Answer: (D) 36
Question: A businessman earns $24800 in December, thus decreasing his average annual (January to December) earnings by $1500. His average annual earnings would be
Source: CMAT Preparation
(A) $29000
(B) $33500
(C) $40200
(D) $41300
(E) $42300
Rationale: (x - 24,800)/11 - x/12 = 1,500
x = 495,600
x/12 = 41,300
Answer: D.
Answer: (D) $41300
Question: The average of six numbers is 3.9. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?
(A) 4.7
(B) 4.45
(C) 4.2
(D) 4.1
(E) 4.9
Rationale: Explanation:
Sum of the remaining two numbers = (3.9 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.40 - (6.8 + 7.7) = 23.40 - 14.5 = 8.90.
Required average = (8.9 / 2) = 4.45.
Answer: B) 4.45
Answer: (B) 4.45
Question: A train of length 250 m runs at a speed of 70 km/hr. What will be the time taken to cross any stationary object standing at the railway station?
(A) 20 sec
(B) 17.23 sec
(C) 12.86 sec
(D) 9.5 sec
(E) 8.5 sec
Rationale: EXPLANATION:
Length of train = 250 m, speed of train = 70 km/hr
Length of train is always considered as distance, and hence here distance = 250 m
1) First convert speed of km/hr into m/s
Speed of train = 70 x	5	= 19.44 m/s
18
2) We know that,
Speed =	Distance /Time
Time taken to cross stationary object =	250 / 19.44
Time taken to cross stationary object= 12.86 sec
ANSWER IS C
Answer: (C) 12.86 sec
Question: if someone is ‘confounded’ means – he is puzzled, confused, bewildered stunned and ‘baffled’. Ask doubt using Question Id: 6320
(A) 21
(B) 87
(C) 278
(D) 277
(E) 261
Rationale: Answer:C
Answer: (C) 278
Question: In a certain government school, 40% of students are below 10 years of age. The number of students above 10 years of age is 5/6 th of the number of students of 10 years age which is 36. What is the total number of students in the school ?
(A) 100
(B) 72
(C) 110
(D) 135
(E) 145
Rationale: Explanation :
Solution: let the number of students be x. then, number of students of or above 10 years = (100-40)% of x = 60% of x.
.'. 60% of x = 36 +5/6 *36
=>60/100 * x = 66
=>x = 110
Answer : C
Answer: (C) 110
Question: The area of a sector of a circle of radius 5 cm formed by an arc of length 5.5 cm is?
(A) 13.78
(B) 13.67
(C) 13.75
(D) 13.98
(E) 13.28
Rationale: (5 * 5.5)/2
= 13.75
Answer:C
Answer: (C) 13.75
Question: What is the smallest no. that should be added to 41381 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, 4+1+3+8+1=17, the next multiple of 9 is 18.
1 must be added to 41381 to make it divisible by 9
A
Answer: (A) 1
Question: A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 4 characters in length. This year, it added the option of creating passwords having 5 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 63 unique alphanumeric case sensitive characters.
(A) 63^4
(B) 62^5
(C) 62(62^4)
(D) 63(62^4)
(E) 64(63^4)
Rationale: Total number of passwords = number of 4 character password +number of 5 character password
= 63^4 + 63^5 (Since there is no limitation on repetition , each character can be chosen in 62 ways )
=63^4(1+ 63)
=63^4 * 64
Answer E
Answer: (E) 64(63^4)
Question: A number a is squared and then multiplied by negative 6. The result of this operation is equal to three times the sum of FOURTH times a and two. What is one possible value of a ?
(A) 2
(B) 3
(C) 4
(D) 1
(E) 5
Rationale: -6*a^2=3(4a+2)
a= -1 or -1
a=-1=B
ANSWER:D
Answer: (D) 1
Question: If a is an integer and b = 3a + 2, which of the following CANNOT be a divisor of b?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Just to add some more to Bunuel's explanation, if a number is a multiple of 3, it will be in a form:
n = 3*k, where k is an integer
And if a number is a multiple of 6, it will be in a form :
m = 6*l, where l is an integer
so m = 2 * 3 * l = (2*l) * 3 = 3 * p, where p is an integer.
In other words, the prime factorization of m must have 3 as a factor, if it's a multiple of 6, but the expression can't have that (as explained by Bunuel), so it can't be a multiple of 6 either.
Answer is A
Answer: (A) 6
Question: Bill has d animals, 32 of which were sold at a profit of 10% each while the rest were sold at a loss of 20% each. Overall, Bill made neither a profit nor a loss. Which of the following is equal to d?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 48
Rationale: Total d animals, suppose each has price of x - total price = dx
now 32 were sold at profit of 10%, making equation - - 32*1.1x
now d-32 were sold at loss of 20%, making eqn --- (d-32)*0.8x
Now he made no profit or loss so,
dx = 32*1.1x + (d-32)*0.8x
solving for d, we get d=48
Ans E
Answer: (E) 48
Question: The volume of a certain substance is always directly proportional to its weight. If 48 cubic inches of the substance weigh 112 ounces, what is the volume, in cubic inches, of 63 ounces of this substance?
(A) 27
(B) 36
(C) 42
(D) 64
(E) 147
Rationale: 112 ounces of a substance has a volume of 48 cubic inches
63 ounces of a substance has a volume of (48/112)*63 = 27 cubic inches
Answer A
Alternatively , we can use estimation
112 ounces of a substance has a volume of 48 cubic inches
56 ounces of a substance has a volume of 24 cubic inches
Therefore , 63 will have a volume a little more than 24 ,that is 27
ANSWER:A
Answer: (A) 27
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money?
(A) 1500
(B) 1992
(C) 9921
(D) 2798
(E) 2789
Rationale: P = 15(100/10)2
=> P = 1500
Answer: A
Answer: (A) 1500
Question: A train which has 600 m long, is running 60 kmph. In what time will it cross a person moving at 6 kmph in same direction ?
(A) 42 sec
(B) 44 sec
(C) 46 sec
(D) 40 sec
(E) 50 sec
Rationale: Time taken to cross a moving person = length of train/ relative speed
Time taken = 600/((60-6) (5/18) = 600/ 54*(5/18) = 600/15= 40 sec
Answer: D
Answer: (D) 40 sec
Question: Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?
(A) 7
(B) 10
(C) 12
(D) 13
(E) 20
Rationale: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.
12-2=10
Option B
Answer: (B) 10
Question: Mohit sold an article for $21000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
(A) 16000
(B) 25000
(C) 15000
(D) 18000
(E) 17500
Rationale: Let the CP be $x.
Had he offered 10% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x = $1.08x = 21000 - 10/100(21000) = 21000 - 2100 = $18900
=> 1.08x = 18900
=> x = 17500
E
Answer: (E) 17500