mathewhe/aqua_rat huggingface dataset:
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?
(A) 27 7/9
(B) 27 7/6
(C) 27 7/2
(D) 27 7/9
(E) 27 7/1
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.
Answer:D
Answer: (D) 27 7/9
Question: P, Q, R enter into a partnership. P initially invests 25 lakh and adds another 10 lakh after one year. Q initially invests 35 lakh and withdraws 10 lakh after 2 years. R's investment is Rs 30 lakh. In what ratio should the profit be divided at the end of 3 years?
(A) 19:18:19
(B) 18:19:19
(C) 19:17:18
(D) 19:19:18
(E) 17:18:19
Rationale: P : Q : R
=(25×1+35×2):(35×2+25×1) :(30×3)
=95:95:90=19:19:18
Answer is D.
Answer: (D) 19:19:18
Question: The sale price of a trolley bag including the sale tax is Rs. 1232. The rate of sale tax is 10% . If the shopkeeper has made a profit of 12%, the cost price of the trolley bag is:
(A) Rs 1000
(B) Rs 1515
(C) Rs 1525
(D) Rs 1250
(E) None of these
Rationale: Explanation :
110% of S.P. = 1232
S.P. = Rs.(1232 x 100/110) = Rs.1120.
C.P. = Rs (100/112 x 1120) = Rs 1000
Answer : A
Answer: (A) Rs 1000
Question: Vishal and Raghu jointly started a business. Vishal invested three times as Raghu did and invested his money for double time as compared to Raghu. Raghu earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was ?
(A) 28,000
(B) 28,129
(C) 28,109
(D) 28,009
(E) 28,011
Rationale: Investments ratio is = 3:1
Time period ratio is = 2:1
As they are proportional to gain
------
Gain ratio of Vishal and raghu = 6:1
But given Raghu got Rs. 4000,
=? 1 ----- 4000
7 ----- ?
=> Rs.28,000
The total gain = Rs.28,000
Answer: A
Answer: (A) 28,000
Question: Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a grey cup, a white cup, and a purple cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?
(A) 150
(B) 160
(C) 200
(D) 180
(E) 240
Rationale: # ways to distribute Blue marbels(3) is :
1 in each cup= 1
2 in one cup and 1 in other=6
all 3 in one cup = 3
total 1+6+3=10 possibilities
# ways to distribute Red marbels(2) is :
1 in each cup = 3 ways
all in one cup = 3ways
total 6ways.
# ways to distribute Green marbels(1) is :
3 ways
total number of ways = 10*6 *3 = 180
D
Answer: (D) 180
Question: The diameter of two circles are 18 cm and 8 cm. The distance between their centres is 13 cm. What is the number of common tangents?
(A) 3
(B) 2
(C) 1
(D) 5
(E) 7
Rationale: A
3
Here, r1 = 9 cm and r 2 = 4 cm
r 1 + r 2 = 9 + 4 = 13 cm
and r 1 – r 2 = 9 – 4 = 5cm
Also, d = 13 cm
Here, d = r 1 + r 2
= 13 cm
Hence, two circles touch each other externally, so three total no of common tangents are three.
Answer: (A) 3
Question: It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?
(A) Sunday
(B) Sarurday
(C) Friday
(D) Wednesday
(E) Monday
Rationale: Explanation:
On 31st December, 2005 it was Saturday. Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days. On 31st December 2009, it was Thursday. Thus, on 1st Jan, 2010 it is Friday.
Answer: C
Answer: (C) Friday
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 752
(B) 799
(C) 719
(D) 750
(E) 712
Rationale: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750
Answer: D
Answer: (D) 750
Question: A train running at the speed of 60 km/hr crosses a pole in 6 seconds. What is the length of the train?
(A) 100
(B) 130
(C) 150
(D) 170
(E) 160
Rationale: Speed=(60x5/18)m/sec = (50/3) m/sec.
Length of the train = (Speed x Time).
Length of the train = (50/3 x 6)m = 100 m.
Answer is A.
Answer: (A) 100
Question: Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 10 percent sulfuric acid, approximately how many liters of the 12 percent solution will be required?
(A) 18
(B) 20
(C) 48
(D) 36
(E) 42
Rationale: let a=amount of 2% acid and b= amount of 12% acid.
Now, The equation translates to,
0.02a + .12b = .1(a+b)
but a+b= 60
therefore .02a + .12b = .1(60)
=> 2a + 12b = 600
but b=60-a
therefore
2a+ 12(60-a) = 600
=> 10a = 120
hence a = 12. b = 60 -12 = 48.
Answer : C
Answer: (C) 48
Question: If after successive discounts of 20% and 25/4% on the marked price of an article, a trader gets 20% profit on the cost price,then by what percent is the marked price above the cost price?
(A) 50%
(B) 60%
(C) 70%
(D) 80%
(E) 90%
Rationale: Let the market price be RS 100. Then after first discount S.P becomes 80 and after another discount it becomes Rs. 75.
so S.P = 75. now with this S.P he has made a profit of 20% and hence the
C.P = (75/120)*100 = 62.5
so percentage change with respect to market price is = (37.5/62.5)*100
giving 60%
ANSWER:B
Answer: (B) 60%
Question: 4/9 × 6/3 + 11/27 – 18/81 = ?
(A) 27(5/24)
(B) 13 (2/7)
(C) 24 (5/27)
(D) 17 (3/21)
(E) None of these
Rationale: Explanation:
= 4/9 × 6/3 + 11/27 – 18/81
=4/9 × 6/3 + 11/27 – 6/27
= 12*54+11-6/27 = 653/27 = 24 (5/27)
Answer: Option C
Answer: (C) 24 (5/27)
Question: When 30 is divided by the positive integer k, the remainder is 6, for how many different values of k is this true?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 8
Rationale: When 30 is divided by k, remainder is 6 i.e. there are 6 balls leftover after grouping. so k must be greater than 6.
It also means that 30 is completely divisible by k.
Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
Out of these, k can be 4, 6, 8, 12, 24.
Answer (C)
Answer: (C) 5
Question: A letter lock consists of three rings each marked with eight different letters. The number of distinct unsuccessful attempts to open the lock is at the most?
(A) 176
(B) 511
(C) 518
(D) 519
(E) 172
Rationale: Since each ring consists of eight different letters, the total number of attempts possible with the three rings is
= 8 * 8 * 8 = 512. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 512 - 1 = 511.
Answer: B
Answer: (B) 511
Question: What least value should be replaced by * in 223*431 so the number become divisible by 9
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Explanation:
Trick: Number is divisible by 9, if sum of all digits is divisible by 9, so (2+2+3+*+4+3+1) = 15+* should be divisible by 9,
15+3 will be divisible by 9,
so that least number is 3.
Answer: Option A
Answer: (A) 3
Question: In a group of 5 boys and 5 girls, four children are to be selected. In how many different ways can they be selected such that at least one girl is included?
(A) 175
(B) 190
(C) 205
(D) 220
(E) 235
Rationale: The total number of ways to choose 4 children is 10C4 = 210
The number of ways to choose only boys is 5C4 = 5
The number of groups which include at least one girl is 205.
The answer is C.
Answer: (C) 205
Question: What is the sum of the integers from -194 to 195 inclusive?
(A) 0
(B) 5
(C) 195
(D) 875
(E) 965
Rationale: sum/n= average.
sum=(average)(n)
average=a+b/2=194+195/2=0.5
number of items(n)=B-A+1=195-(-194)+1=195+195=390.
sum=average*n=0.5*390=195.
answer is C
Answer: (C) 195
Question: If a man buys 10 lollipops for $80 and sold them for $2 dollars determine his loss.
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: Cost of 10 lollipops = $80
Sold each lollipop for $2
So, he sold 10 lollipops for $(10 × 2) = $20
Loss = $(80 – 20) = $60
answer :B
Therefore, loss = $ 60.
Answer: (B) 60
Question: What is the tens' digit R of the sum of the first 40 terms of 1, 11, 111, 1111, 11111, 111111, ...?
(A) R=2
(B) R=3
(C) R=4
(D) 8
(E) 9
Rationale: All of the first 40 terms have 1 at the units place.
Except the first term, the tens digit of all the remaining 39 terms is 1.
So now if you do the addition
1 1
1 1
. . .
. . .
. . .
1 1
0 1
3 0
Answer is B
Answer: (B) R=3
Question: On flipping 3 coins together what is the outcomes for at least two tails?
(A) {HHH, HHT, HTH, THH}
(B) {HHT, HHT, HTH, THH}
(C) {TTH, HHT, HTH, THH}
(D) {TTH,THT, HTT,TTT}
(E) None
Rationale: Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Favorable outcomes for at least two tails
= favorable outcomes for exactly two heads and favorable outcomes for more than two heads
= {TTH, THT, HTT, TTT}
D
Answer: (D) {TTH,THT, HTT,TTT}
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
(A) 3
(B) 4
(C) 2
(D) 5
(E) 7
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer: A
Answer: (A) 3
Question: If the operation ∆ is defined by a ∆ b = (b - a)^2/a^2 for all numbers a and b, and a ≠ 0, then what is the result when we evaluate this expression: (-6) ∆ (6 ∆ −6) ?
(A) 36/25
(B) 81/4
(C) 25/4
(D) 49/9
(E) 25/9
Rationale: (-6) ∆ (6 ∆ −6) =
(-6) ∆ (12^2/6^2) =
(-6) ∆ (4) =
(-10^2) / (-6)^2 = 100/36 = 25/9
The answer is E.
Answer: (E) 25/9
Question: The average of five results is 46 and that of the first four is 35. The fifth result is?
(A) 50
(B) 90
(C) 77
(D) 66
(E) 51
Rationale: 5 * 46 â€“ 4 * 35
= 90
Answer: B
Answer: (B) 90
Question: Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
(A) 1by7
(B) 1/8
(C) 1/9
(D) 7/8
(E) 1/5
Rationale: Original share of 1 person = 1/8
New share of 1 person = 1/7
Increase =(1/7-1/8) = 1/56
Required fraction = (1/56)/(1/8)
= (1/56)*8
= 1/7
ANSWER:A
Answer: (A) 1by7
Question: A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of r square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1 mile = 5,280 feet and 1 foot = 12 inches)
(A) (5,280 mt) / 12 r
(B) (5,280 pt) / 12m
(C) (5,280 pmt) /12
(D) (5,280)(12m) / pt
(E) (5,280)(12p) / mt
Rationale: Given that: 1 gallon of paint covers an area ofrsquare feet. Question:how many gallonsof paint will be needed ...
In any case you will have:(total area in square feet)/(gallons per feet)=(total area in square feet)/r, so r must be in the denominator: eliminate all but A and D.
Now, lets see where should be t: (area in square feet)=(width in feet)*(length in feet) --> width=tinchesas1 feet=12 inchesthent inches=t/12 feet, so (area in square feet)=(t/12) * (length in feet), so t must be in the nominator: only A is left.
Answer: A.
Answer: (A) (5,280 mt) / 12 r
Question: The ratio of men to women in the Snyder community choir is 4 to 7. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many women are in the Snyder choir?
(A) 20
(B) 24
(C) 28
(D) 32
(E) 34
Rationale: This question has a number of patterns in it that we can take advantage of. We can also TEST THE ANSWERS (but we can actually eliminate most of the answer choices rather quickly.
We're told that the ratio of the Men to Women in the Snyder choir is 4 to 7, so the number of men MUST be a multiple of 4 and the number of women MUST be a multiple of 4 The question asks how many WOMEN are in the SNYDER choir, so the answer MUST be a multiple of 7. We can eliminate AnswersA, B, D and E (since they're NOT multiples of 7
Answer C
Answer: (C) 28
Question: The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?
(A) 78
(B) 54
(C) 96
(D) Cannot be determined
(E) 56
Rationale: Answer: Option D
Let the ten's digit be x and unit's digit by y
Then, x + y = 15 and x - y = 3 or y - x = 3
Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6
Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9
So, the number is either 96 or 69.
Hence, the number cannot be determined.
Answer: (D) Cannot be determined
Question: If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of;
6 – 9 + 8 × 3 ÷ 25 =
(A) 6
(B) 10
(C) 12
(D) 5
(E) 8
Rationale: D 5
Answer: (D) 5
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
(A) 22
(B) 32
(C) 77
(D) 66
(E) 8
Rationale: A/8 = 8 * 8 => A = 8 * 8 * 8
x * 2x = 8 * 8 * 8
x = 16 => 2x = 32
nswer: B
Answer: (B) 32
Question: In store A there are 10 pairs of pants for every 50 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?
(A) 3:16.
(B) 2:3.
(C) 4:15.
(D) 3:4.
(E) 2:5.
Rationale: 1st statement : ratio of pants
Store A : Store B
10x : 50x
X:5X
Price :
4y:3y
Total revenue
4xy : 15xy
4:15
Answer : C
Answer: (C) 4:15.
Question: The area of one square is x^2 + 6x + 9 and the area of another square is 4x^2 − 20x + 25. If the sum of the perimeters of both squares is 52, what is the value of x?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: The areas are (x+3)^2 and (2x-5)^2.
The lengths of the sides are x+3 and 2x-5.
If we add the two perimeters:
4(x+3) + 4(2x-5) = 52
12x = 60
x = 5
The answer is C.
Answer: (C) 5
Question: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer V that must divide n is?
(A) 6
(B) 12
(C) 24
(D) 36
(E) 48
Rationale: Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer V that must divide n is:
A 6, B 12, C 24, D 36, E 48
n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied by 2, it will be (2)(8)(9) = (16)(9) = 144, a perfect square. So n^2 must be at least 144 or a multiple of 144, which means that n must be 12 or a multiple of 12.B
Answer: (B) 12
Question: Find the value of x in 5(x+4)=25
(A) 1
(B) 1.5
(C) 2
(D) 2.5
(E) 3
Rationale: 5(x+4)=25
Dividing both sides by 5 gives (x+4)=5
Subtracing both sides with 4 gives x=1
Answer: A
Answer: (A) 1
Question: When positive integer D is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when D is divided by B?
(A)  13
(B)  14
(C)  15
(D)  16
(E)  17
Rationale: the remainder will be obtained from the decimal part when D is divided by B i.e. 0.35
0.35 = 35/100 = 7/20 so possible remainders are 7,14,21,28. Only option B-14 satisfies this
PS: for B-14 D=174 and B=40
Answer: (B)  14
Question: Jancy invested an amount of Rs. 9,000 at the rate of 10% p.a simple interest and another amount at the rate of 15% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested?
(A) 15800
(B) 12800
(C) 11800
(D) 16800
(E) 17800
Rationale: Let the second amount be Rs. x. Then,
(9000 * 10 * 1)/100 + (x * 15 * 1)/100 = [(12000 + x) * 14 * 1] / 100
9000+ 15x= 16800 + 14x
x = 7800
Total investment = 10000 + 7800 = Rs. 17,800.Answer: E
Answer: (E) 17800
Question: How many different eight letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?
(A) 59
(B) 11!/(2!*2!*2!)
(C) 56
(D) 76
(E) 11!/(3!*2!*2!*2!)
Rationale: E- -R
We are left with the following 11 letters: {M, D, I, T, R, EE, AA, NN} out of which 8 are distinct: {M, D, I, T, R, E, A, N}.
We should consider two cases:
1. If the two middle letters are the same, we'd have 3 words: EEER, EAAR and ENNR.
2. If the two middle letters are distinct, then we are basically choosing 2 letters out of 8 when the order of the selection matters, so it's 8P2 = 56.
Total = 56 + 3 = 76.
Answer: D.
Answer: (D) 76
Question: Z is a set of positive numbers. The median of Z is greater than the mean of Z. Which of the following R must be true?
I. At least 50% of the numbers in Z are smaller than the median.
II. Less than 50% of the numbers in Z are greater than the median.
III. The median of Z is greater than the average of the largest and smallest numbers in Z.
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) R=None of the above
Rationale: Condition 3 can be invalidated by: (1, 3, 4, 5)--median is equal to average of 1 and 5 and average is greater than 3.
Then, don't conditions 1 and 2 have to occur simultaneously? I reasoned this based on the word... maybe that's incorrect.
Even if not, we can rule them both out. So, E.
Answer: (E) R=None of the above
Question: Tom, working alone, can paint a room in 8 hours. Peter and John, working independently, can paint the same room in 4 hours and 2 hours, respectively. Tom starts painting the room and works on his own for two hour. He is then joined by Peter and they work together for two hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?
(A) 4/7
(B) 5/7
(C) 6/7
(D) 1/7
(E) 3/7
Rationale: Let the time when all three were working together be t hours. Then:
Tom worked for t+4 hour and has done 1/8*(t+4) part of the job;
Peter worked for t+2 hour and has done 1/4*(t+2) part of the job;
John worked for t hours and has done 1/2*t part of the job:
1/8*(t+4)+1/4*(t+2)+1/2*t=1 --> multiply by 8 --> (t+4)+(2t+2)+4t=8 --> t=2/7;
Hence Peter has done 1/4*(2/7+2)=1/4 *16/7=16/28 =8/14 =4/7
Answer: A
Answer: (A) 4/7
Question: 1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now?
(A) 76 days
(B) 98 days
(C) 32 days
(D) 45 days
(E) 24 days
Rationale: 1600 ---- 28 days
1600 ---- 24
1200 ---- ?
1600*24 = 1200*x
x = 32 days
Answer: C
Answer: (C) 32 days
Question: Calculate the largest 3 digit number which is exactly divisible by 89?
(A) 911
(B) 969
(C) 979
(D) 977
(E) 971
Rationale: Largest 4 digit number is 999
After doing 999 ÷ 89 we get remainder 20
Hence largest 3 digit number exactly divisible by 89 = 999 - 20 = 979
C
Answer: (C) 979
Question: If a, b are integers and |a-b|=12, which of the following is the smallest possible value of ab?
(A) -16
(B) 0
(C) -36
(D) 7
(E) 40
Rationale: a=6, b=-6. Hence, the answer is C.
Answer: (C) -36
Question: Find the sum of first 80 odd numbers
(A) 6400
(B) 8000
(C) 5000
(D) 4980
(E) 4960
Rationale: Explanation:
n2 = 802 = 6400
Answer: Option A
Answer: (A) 6400
Question: Robert is travelling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m.?
(A) 17 kmph
(B) 19 kmph
(C) 15 kmph
(D) 12 kmph
(E) 16 kmph
Rationale: D
12 kmph
Let the distance traveled be x km.
Then, x/10 - x/15 = 2
3x - 2x = 60 => x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60/10 = 6 hrs.
So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.
Required speed = 60/5 = 12 kmph.
Answer: (D) 12 kmph
Question: Two cards are drawn from a pack of well shuffled cards. Find the probability that one is a club and other in King
(A) 1/29
(B) 1/26
(C) 1/26
(D) 1/25
(E) 1/22
Rationale: Explanation:
Let X be the event that cards are in a club which is not king and other is the king of club.
Let Y be the event that one is any club card and other is a non-club king.
Hence, required probability:
=P(A)+P(B)
=\inline {\color{Black}[(12C_{1}\times 1C_{1})/52C_{2}]+[(13C_{1}\times 3C_{1})/52C_{2}]}
Answer: B) 1/26
== =
Answer: (B) 1/26
Question: Find the constant k so that : -x2 - (k + 10)x - 8 = -(x - 2)(x - 4)
(A) 11
(B) 12
(C) 16
(D) 14
(E) 15
Rationale: -x2 - (k + 10)x - 8 = -(x - 2)(x - 4) : given
-x2 - (k + 10)x - 8 = -x2 + 6x - 8
-(k + 10) = 6 : two polynomials are equal if their corresponding coefficients are equal.
k = -16 : solve the above for k
correct answer C
Answer: (C) 16
Question: Multiply: (x – 4)(x + 5)
(A) (a) x2 + 5x - 20
(B) (b) x2 - 4x - 20
(C) (c) x2 - x - 20
(D) (d) x2 + x - 20
(E) (e) x2 + x + 20
Rationale: (x – 4)(x + 5).
= x(x + 5) -4(x + 5).
= x2 + 5x – 4x – 20.
= x2 + x - 20
the answer is (D)
Answer: (D) (d) x2 + x - 20
Question: A computer store originally bought 1,000 modems at a total cost of d dollars. If each modem was sold for 25 percent more than its original cost, what was the individual price, in terms of d, of each modem sold?
(A)  d/800
(B)  5d/1000
(C)  125d
(D)  d/1000 + 25
(E)  125/(1000d)
Rationale: Since you're choosing to approach this algebraically, I'm going to add some labeling to your work....
1,000 purchased for a total of D dollars.....
Each modem costs D/1,000 dollars....
Each modem is then sold for 25% ABOVE the cost:
(1.25)(D/1,000) = 1.25D/1,000
1.25D/1,000 = 125D/100,000
125/1,000 = 1/8 so....
125/100,000 = 1/800
So the sell price of each modem is D/800
Final Answer:
A
Answer: (A)  d/800
Question: John went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) A)19.7
(B) B)21
(C) C)21.4
(D) D)21.5
(E) E)22.5
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total ta x incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
A
Answer: (A) A)19.7
Question: A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 4 minutes?
(A) 36
(B) 54
(C) 108
(D) 216
(E) 324
Rationale: Direct Relationship:-
1 standard Veggiematik machine - 36 Carrots - 4 minutes,
1 standard Veggiematik machine - 9 Carrots - 1 minute,
Now
6 standard Veggiematik machine - ? Carrots - 4 minutes,
Hence = 9X6X4 =216 Carrots
Answer D
Answer: (D) 216
Question: In a 100 metre race, A can allow B to start the race either 10 metres ahead of the starting point or 2 seconds before A so that both reach the finishing line at the same time. What is the speed of B in m/sec and how long will A take to run 100 m?
(A) 6 m/sec; 18 sec
(B) 5 m/s; 18 sec
(C) 4 m/s; 15 sec
(D) 3 m/s; 12 secs
(E) 2 m/s; 6 secs
Rationale: A can allow B to start the race 10 metres ahead, so the time A need to cover 100 meters equals to the time B needs to cover 90 meters --> 100/a = 90/b, where a and b are the rates of A and B, respectively.
A can allow B to start the race 2 seconds before A, so the time A need to cover 100 meters is 2 seconds less than the time B needs to cover 100 meters --> 100/a + 2 = 100/b.
Subtract one from another: 2 = 100/b - 90/b --> b = 5.
Answer: B.
Or directly: B needs 2 seconds more to cover 100 meters than to cover 90 meters --> 2 = 100/b - 90/b --> b = 5.
Answer: (B) 5 m/s; 18 sec
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 21 months?
(A) 18:11
(B) 18:15
(C) 21:11
(D) 18:121
(E) 18:112
Rationale: A invests Rs.8000 for 21 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*21 : (8000*4) + (4000*14)
168000 : 88000
A:B = 21:11.Answer:C
Answer: (C) 21:11