MU-NLPC/Calc-aqua_rat huggingface dataset:
The post office processed lots of packages every weekday. The numbers of packages it processed per day were 80, 30, 100, 90 and x. If the median number of packages was 10 higher than the average (arithmetic mean) number of packages, which of the following could be x? Choices
A) 40  B) 45  C) 50  D) 55  E) 60

Solution: Look at the options available   Value of x seems to 40 < = x < = 60   A. 40   B. 45   C. 50   D. 55   E. 60   So position of x is second   30 , x , 75 , 85 , 95   Median = 75   Median number of packages was 10 points higher than the average, so average = 65   30 + x + 75 + 85 + 95 = 325   x = 40 = 40nswer = 40
Answer: A
What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58? Choose the correct answer:
A) Rs.3944
B) Rs.3943
C) Rs.3928
D) Rs.3929
E) Rs.3925

Solution: Let the side of the square plot be a ft.   a2 = 289 => a = 17   Length of the fence = Perimeter of the plot = 4a = 68 ft.   Cost of building the fence = 68 * 58   = Rs.3944.   Rs.3944nswer:Rs.3944
Answer: A
If there are 5 seats and 2 students, in how many ways can they be seated?	Choose one:  A) 12  B) 16  C) 20  D) 24  E) 28

Solution: The first student has 5 choices and the second student has 4 choices.   The number of ways to sit is   5*4= 
  5*4 = 20
20.   The answer is 20.
Answer: C
When positive integer x is divided by positive integer y, the result is 59.32. What is the sum W of all possible 2-digit remainders for x/y?	Choose the correct choice from the following answers:  A) 560  B) 616  C) 672  D) 728  E) 784

Solution: ans B 616...   remainders = .32=32/100=8/25=16/50 and so on..   so two digit remainders are 16+24+32+....+96..   W=8(2+3+4....+12)=616
Answer: B
A corporation triples its annual bonus to 50 of its employees. What percent E of the employees’ new bonus is the increase? Choose the correct choice
A) 50%	B) 662⁄3%	C) 100%	D) 200%	E) 300%

Solution: E of the employees’ new bonus is the increase Hence 662⁄3%.
Answer: B
The ratio of 2 numbers is 1:2 and their H.C.F. is 10. Their L.C.M. is ?
Choose the correct choice from the following answers:	A) 10	B) 20	C) 30	D) 50	E) 40

Solution: Let the numbers be x and 2x   Their H.C.F. = 10   so the numbers are 1*10 , 2*10 = 10,20   L.C.M. = 20   Answer is 20
Answer: B
Tea worth Rs. 126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg
Answers:
A) 175.59
B) 175.5
C) 175.57
D) 175.52
E) 175.11

Solution: Explanation:   Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50   So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.   Cost of 1 kg tea of 1st kind Cost of 1 kg tea of 2nd kind   x-153/22.50 = 1 => x - 153 = 22.50 => x=175.50.   Hence, price of the third variety = Rs.175.50 per kg.   Answer: C) Rs. 175.50
Answer: C
The 1:30 pm train leaves the station as a prospective passenger reaches the platform. Assuming that the train is going at 40 kmph, and the next train is an Express leaving half an hour later, which will go 50 kmph, when will the passenger reach the same place as the train he missed? Select:
A) 2:00 pm  B) 2:30 pm  C) 3:45 pm  D) 4:00 pm  E) 5:15 pm

Solution: Distance covered by the original train in 1/2 hour = 20 km   10 km is compensated for in 1 hour, therefore 20 km will be compensated in 2 hours   So, the Express overtakes the original train at 4 p.m.   Correct Answer: 4:00 pm
Answer: D
If y is the smallest positive integer such that 6300 multiplied by y is the square of an integer, then y must be
Choose the correct choice from the following answers
A) 5 B) 7 C) 15 D) 35 E) 45

Solution: 6300 = 2^2*3^2*5^2*7   To be perfect square, we need to multiply by at least 7.   The answer is 7.
Answer: B
From January through June, 46200 immigrants applied for citizenship. During this same period last year, 120000 immigrants applied. What is the percentage of decrease? Choose the correct choice from the following choices
A) 38.5
B) 38.6
C) 38.7
D) 38.8
E) None

Solution: Solution:   (46200/120000) * 100 = 462/12= 
462/12 = 77/2 = around 38.5
38.5   38.5nswer 38.5
Answer: A
If x ¤ y = (x + y)^2 - (x - y)^2. Then √5 ¤ √5 = Choices.
A) 0	B) 5	C) 10	D) 15	E) 20

Solution: X = √5 and Y also =√5   Applying the function (√5+√5)^2 - (√5-√5)^2 = (2√5)^2 - 0 = 4 x 5 = 20.   Note: Alternative Approach is the entire function is represented as X^2 - Y^2 = (X+Y)(X-Y) which can be simplified as (x+y+x-y)(x+y-(x-y)) = (2x)(2y)=4xy. Substituting x=√5 and y = √5 you get the answer 20   Answer is 20.
Answer: E
The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?  Choose the most appropriate option:	A) 23	B) 1:2	C) 2:5	D) 3:5	E) 25

Solution: C   C.P. = Rs. 5x and S.P. = Rs. 7x.   Then, Gain = Rs. 2x   Required ratio = 2x : 5x = 2:5
Answer: C
In a class of students, 1/2 of the number of girls is equal to 1/3 of the total number of students. What is the ratio of boys to girls in the class?
Choose the correct answer
A) 1/2
B) 1/3
C) 2/3
D) 1/4
E) 3/4

Solution: (1/2)G=(1/3)(B+G)   3G=2B+2G   G=2B   B/G=1/2.   The answer is 1/2.
Answer: A
The length and the breadth of a rectangle are in the ratio of 3 : 2 respectively. If the sides of the rectangle are extended on each side by 1 metre, the ratio of length to breadth becomes 10 : 7. Find the area of the original rectangle in square metres. Choose the correct choice from the following answers:  A) 256  B) 150  C) 280  D) Data inadequate  E) None of these

Solution: Let the length and breadth be l and b respectively.   l⁄b = 3⁄2 or l = 3⁄2b .....(i)   l+1/b+1=10/7 or 7l - 10b = 3 .....(ii)   From eq. (i)   10.5b – l 0b = 6 or, 0.5b = 3 or, b = 6 and l = 9   Area = l × b = 6 × 9 = 54 m2   Answer None of these
Answer: E
If m > 0 and x is m/10 of y, then, in terms of m, y=?x  Select.
A) a) 100m
B) b) 1/100m
C) c) 1/m
D) d) 100/m
E) e) 10,000/m

Solution: x= m/10 * y   So y= 10/m * x   So y= (100/m)/10 * x   d) 100/m
Answer: D
The ratio of boys to girls in Class A is 5 to 4. The ratio of boys to girls in Class B is 4 to 5. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?
Select.
A) 8
B) 7
C) 10
D) 11
E) 12

Solution: Since it is given that the ratio of boys to girls in Class A is 3 to 4 - so we can quickly eliminate the answer choices which are not multiples of 4.   so ans can either be 8 0r 12.   With 8 as answer - no of girls = 8   With 12 as answer - no of girls = 12   Now Class A has one more boy and two more girls than class B and also the ratio of boys to girls in Class B is 4 to 5.   So we are looking for number of girls in B to be divisible by 5.   With 8 as answer -> Girls = 8-2= 
8-2 = 6
6. (Not possible)   With 12 as answer -> Girls= 12-2 = 5.   So, answer = 7. ( 7)
Answer: B
According to the formula F=9/5 (C) +32, if the temperature in degrees Farenheit (F) increases by 29, by how much does the temperature in degrees Celsius (C) increase?	Pick one.
A) 9
B) 15
C) 47
D) 48 3/5
E) 59

Solution: You can plug in values.   C = 5/9*(F-32)   F=32 --> C=0;   F=32+29= 
32+29 = 61
61 --> C=5/9*29=16.11.   Increase = 16.11 degrees.   Answer: 15.
Answer: B
Find a a prime number from the options below.	Choose the correct choice from the following:	A) 86	B) 87	C) 88	D) 89	E) 90

Solution: Clearly, 89 is a prime number.   89
Answer: D
If an integer x is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that x(x + 1)(x + 2) will be divisible by 8? Choose the correct choice from the following answers: A) 1/4 B) 3/8 C) 1/2 D) 5/4 E) 5/8

Solution: I get 5/8 as well   1 to 96 inclusive means we have 48 odd and 48 even integers   5/8 O 5/8 / 8 = Integer, therefore we have 48 / 96 numbers divisible by 8   O 5/8 O / 8 = Not Integer   We cannot forget multiples of 8 from 1 to 96   We have 12 numbers that are multiple of 8   Therefore, 48/96 + 12/96 = 60/96 = 5/8   answer : 5/8
Answer: E
9 friends are living in 9 different flats of an apartment. Each of them was allotted a parking spot to park their cars in the ground floor. But they used to park their cars randomly in any of the 9 parking spots. In how many ways can they park their cars so that exactly 7 people park their cars in the spots allotted to them?  Choices.
A) 24
B) 36
C) 48
D) 60
E) 72

Solution: 9C7 = 36   The remaining 2 people in each case will be parked in each other's parking spots.   The answer is 36.
Answer: B
Machine A can print one lakh books in 8 hours. Machine B can do the same job in 10 hours. Machine C can do the same job in 12 hours. All the three machines start job at 9.00 am. A breaks down at 11.00 am and the other two machines finish the job. Approximately at what time will the job be finished?	Answers:
A) 12.00 noon
B) 1.30 pm
C) 1.00 pm
D) 11.30 am
E) None of these

Solution: Part of print done by A, B and C in 2 hours = 2(1⁄8 + 1⁄10 + 1⁄12) = 37⁄60   Remaining = 1 - 37⁄60 = 23⁄60   If B and C print together, then they can print in 10×12/10+12   Therefore, remaining part can be printed by   B and C in 10×12/22×23/60 ≈ 2 hrs.   Hence, the job will be finished at   9 am + 2 + 2 = 1.00 p.m.   Answer 1.00 pm
Answer: C
A coin is tossed 5 times, Probability of getting
head exactly 3 times is: Choose the correct choice from the following answers
A) 0.3125
B) 0.4125
C) 0.5125
D) 0.6125
E) 0.7125

Solution: coin tossed 5 times so  2*2*2*2*2= 
 2*2*2*2*2 = 32
32   getting heads only in 3 times=HHHHH,HHHHT,HHHTT,HHTTH,HTTHH,TTHHH,THHHT,THHTH,THTHH,HTHTH=10   PROBABILITY=10/32=0.3125.   0.3125NSWER:0.3125
Answer: A
In a LAB experiment, a 100 ml compound of element X and element Y needs to be increased to 150 ml by adding some quantity of element X, and some quantity of element Y. If the original compound contains 30% of element X, how much (in ml) of element Y must be added so that element X will be exactly one third of the resulting mixture ?
Choose the correct choice from the following options
A) 40 ml	B) 100/3 ml	C) 30 ml	D) 20/3 ml	E) 10 ml

Solution: There are 0.3*100= 
0.3*100 = 30
30 ml of element X in the initial solution.   We need X to be 1/3rd of 150 ml in the resulting solution, so 50 ml. Thus out of 50 ml of solution added, 20 must be X (in order it to become 50 ml) ans the remaining 30 must be Y.   Answer: 30 ml
Answer: C
A milk man makes a profit of 20% on the sale of milk. If he were to add 10% water to the milk, by what % would his profit increase?  Pick:
A) 30
B) 40⁄3
C) 22
D) 10
E) None of these

Solution: Let profit per litre = 20   So, C.P. /litre = 100   S.P. / litre = 120   On adding 10% water to the milk   C.P. / 9⁄10 litre = 100   S.P. / 9⁄10 litre = 120   S.P / litre = 120×10/9=400/3   ⇒ Profit / litre = 400⁄3 - 100 = 33.33   % by which profit increases = 33.33 – 20 = 13.3   Answer 40⁄3
Answer: B
What least number must be added to 696, so that the sum is completely divisible by 20 ?	Choose the correct choice from the following answers
A) 2	B) 4	C) 3	D) 5	E) 6

Solution: If we divide 696 by 20 remainder is 16   20 - 16= 
20 - 16 = 4
4   Answer : 4
Answer: B
The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?  Choose the correct choice from the following options
A) Rs.17	B) Rs.12	C) Rs.15	D) Rs.29	E) Rs.19

Solution: Total members in the group = 7   Average amount = Rs. 20   Total amount with them = 7 * 20 = Rs. 140   One number has Rs. 50. So, the amount with remaining 6 people = 140 - 50 = Rs. 90   The average amount with them = 90/6   = Rs.15.   Answer:Rs.15
Answer: C
Replace the ? by the correct Mathematics symbol to make the expression true 15 ? 3 ? 3 ? 5 = 20	Choices:
A) 15 ÷ 3 x 3 - 5 = 20  B) 15 + 3 ÷ 3 + 5 = 20  C) 15 x 3 + 3 + 5 = 20  D) 15 x 3 ÷ 3 + 6 = 20  E) 15 x 3 ÷ 3 + 5 = 20

Solution: Answer : 15 x 3 ÷ 3 + 5 = 20
Answer: E
Two right circular cylinders of equal volumes have their heights in the ratio 1:2. Find the ratio of their radii.	Choose the correct choice from the following answers
A) √3:1  B) √7:1  C) √2:1  D) 2:1  E) 3:1

Solution: Explanation:   Let their heights be h and 2h and radii be r and R respectively then.   πr2h=πR2(2h)   =>r2/R2 = 2h/h   =2/1   =>r/R = √2/1   =>r:R = √2:1   ANSWER IS √2:1
Answer: C
How many positive integers less than 15 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?
Pick.
A) 14  B) 13  C) 12  D) 8  E) 10

Solution: The number = 2a + 3b < 20   When a = 1, b = 1, 2, 3, 4, 5 -> 2a = 2; 3b = 3, 6, 9-> the number = 5, 8, 11 --> 3 numbers   when a =2, b = 1,2,3-> ....--> 3 numbers   when a =3, b = 1,2,3,4 --> ....--> 2 numbers   Total number is already 8. Look at the answer there is no number greater than 8 --> we dont need to try any more   Answer must be 8
Answer: D
If [x] is the greatest integer less than or equal to x, what is the value of [-2.6]+[1.4]+[2.7]?	Choose the most appropriate option
A) 0	B) 1	C) 2	D) 6	E) 7

Solution: You are asked what the closest lesser integer value to [x] is.   [-2.6] = -3.0   [1.4] = 1.0   [2.7] = 2.0   Therefore , answer is: -3.0 + 1.0 + 2.0= 
-3.0 + 1.0 + 2.0 = 0
0.0   Option 0.
Answer: A
A train 125 m long passes a man, running at 4 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Choose the most appropriate option
A) 11  B) 49  C) 88  D) 65  E) 22

Solution: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr   = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 4) km/hr. x - 4 = 45 ==> x   = 49 km/hr.   Answer:49
Answer: B
What is the remainder when 1201 × 1202 ×1203 × 1204 is divided by 6?  Pick one.
A) 0 B) 1 C) 2 D) 3 E) 4

Solution: The remainders when dividing each number by six are: 1, 2, 3, and 4.   The product is 1*2*3*4= 
1*2*3*4 = 24
24   The remainder when dividing 24 by 6 is 0.   The answer is 0.
Answer: A
A person buys an article at $1200. At what price should he sell the article so as to make a profit of 40%?
Answers:
A) 1670  B) 1600  C) 1680  D) 1900  E) 1230

Solution: 1680   1680   1680ost price = $1200   profit = 40% of 1200 = $480   Selling price = 1680ost price + Profit   = 1200 + 480= 
1200 + 480 = 1_680
1680
Answer: C
There is a sufficient food for 200 men for 20 days after 15 days 100 men leave the place. For how many days will the rest of the food last for the rest of the men?
Choose the correct choice from the following:
A) 10 days
B) 5 days
C) 15 days
D) 12 days
E) 10 days

Solution: Explanation:   10 daysfter 13 days , 100 men left,   Therefore 5 days*200 men =x days*100men   X = 10 days   10 daysnswer: Option 10 days
Answer: A
Nelly made a part payment of $875 toward buying a brand new refrigerator, which represents 25% of the total cost of the refrigerator, how much remains to be paid?  Choose the correct choice from the following options.
A) $2225  B) $2782  C) $1625  D) $2629  E) $2625

Solution: Explanation:   Let's start with what the total price of the refrigerator would be. If 25% is equal to $875 then 100% equals $x. We just have to multiply $875 by 4 to get total amount=$3500. Out of this amount we then need to deduct the amount already paid which was $875 so we have $3500-$875=$2625   Answer: Option $2625 3500- 875= 
 3500- 875 = 2_625
$2625   Answer: Option $2625
Answer: E
Salesperson A's compensation for any week is $260 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of B's total sales for that week. For what amount of total weekly sales would both salespeople earn the same compensation? Choose the correct choice from the following answers.
A) $6000  B) $8000  C) $10,000  D) $12,000  E) $14,000

Solution: 260+0.06(x-1000) = 0.08x   0.02x = 200   x = $10,000   The answer is $10,000.
Answer: C
A man travelled a distance of 80 km in 7 hours partly on foot at the rate of 8 km per hour and partly on bicycle at 16 km per hour. Find the distance travelled on foot.
Choose the correct choice:
A) 26 km B) 32 km C) 30 km D) 28 km E) None

Solution: Total Time = 7hrs   Let the distance travelled by foot @ 8kmph be x kms   ? distance travlled by bicycle @ 16kmph be (80-x)kms   ATQ. 7hr = x/8 + (80-x)/16   ? 7 = (2x + 80 - x)/16   ? x = 32kms   Answer: 32 km.
Answer: B
Express a speed of 30 kmph in meters per second?
Choose the correct choice from the following:
A) 10 mps B) 8 mps C) 9 mps D) 7 mps E) 12 mps

Solution: 30 * 5/18   = 8 mps   Answer:8 mps
Answer: B
Anusha, Banu and Esha run a running race of 100 meters. Anusha is the fastest followed by Banu and then Esha. Anusha, Banu and Esha maintain constant speeds during the entire race. When Anusha reached the goal post, Banu was 10m behind. When Banu reached the goal post Esha was 10m behind. How far was behind Anusha when the latter reached the goal post.  Choose the most appropriate option:
A) 22 B) 88 C) 81 D) 66 E) 22

Solution: By that time Anusha covered 100m, Bhanu covered 90m. So ratio of their speeds = 10 : 9   By that time Bhanu reached 100m, Esha covered 90m. So ratio of their speeds = 10 : 9   Ratio of the speed of all the three = 100 : 90 : 81   By that time Anusha covered 100m, Esha Covers only 81.   Answer:81
Answer: C
A distributor sells a product through an on-line store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $15 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 35% profit on the cost of the item? Choose the correct choice from the following choices:
A) 18 B) 21.6 C) 22 D) 22.5 E) 27.7

Solution: Producer price = $15;   The distributor wants to maintain a 20% profit on the cost of the item, thus he must get $ 15*1.2= 
 15*1.2 = 18
$18 after the store takes a commission of 35% of the final price --> (final price)*0.65= $18 --> (final price) = $27.7.   Answer: 27.7.
Answer: E
n^(n/2)=2 is true when n=2 in the same way what is the value of n if n^(n/2) =12?  Options.
A) 12
B) 6
C) 14
D) 16
E) 10

Solution: n^(n/2)=1212pply logN/2logn=log12nlogn=2log12=log12^2=log144Logn=log144Now apply antilogn= 144/nNow n=1212NSWER:12
Answer: A
A, B, K start from the same place and travel in the same direction at speeds of 30km/hr, 40km/hr, 60km/hr respectively. B starts five hours after A. If B and K overtake A at the same instant, how many hours after A did K start?  Choose the correct answer:
A) 3
B) 4.5
C) 4
D) d) 10
E) e) 5

Solution: The table you made doesn't make sense to me. All three meet at the same point means the distance they cover is the same.   We know their rates are 30, 40 and 60.   Say the time taken by B is T hrs. Then A takes 5+T hrs. And we need to find the time taken by K.   Distance covered by A = Distance covered by B   30*(5+T) = 40*T   T = 15 hrs   Distance covered by B = Distance covered by K   40*T = 60*Time taken by K   Time taken by K = 40*15/60= 
40*15/60 = 10
10 hrs   Time taken by A= 5+T = 5+15= 
5+15 = 20
20 hrs   Time taken by K= 10 hrs   So K starts  20-10= 
 20-10 = 10
10 hrs after A. (answer d) 10)
Answer: D
What is the product of the greatest 2 digit multiple of 5 and the greatest 2 digit prime number?
Pick one:
A) 9,310  B) 9,408  C) 9,506  D) 9,603  E) 9,702

Solution: the greatest 2 digit multiple of 5: 95   the greatest 2 digit prime numebr: 97   97*98.   9,310)9,310
Answer: A
How many possible ways are there to select 2 stocks at random from 11 stocks?
Choose the correct choice from the following answers:
A) 35
B) 40
C) 45
D) 50
E) 55

Solution: 11C2 = 55   The answer is 55.
Answer: E
If the true discount on s sum due 2 years hence at 14% per annum be Rs. 168, the sum due is ?
Select the correct option.
A) 948 B) 876 C) 768 D) 658 E) 958

Solution: P.W. = (100*T.D)/(R*T) = (100*168)/(14*2)= 
(100*168)/(14*2) = 600
600 Sum= (P.W. + T.D.) = Rs. (600 + 168) = Rs. 768. Answer : 768
Answer: C
Ada's income is 60 percent more than Adelaide's income, and Adelaide's income is 50 percent less than Bella's income. What percent of Bella's income is Ada's income?	Choose the correct choice from the following:
A) 86%
B) 30%
C) 50%
D) 90%
E) 80%

Solution: Bella's income = 100 (assume);   Adelaide's income = 50 (50 percent less than Bella's income);   Ada's income = 80 (60 percent more than Adelaide's income).   Thus, Ada's income (80) is 80% of Bella's income (100).   Answer: 80%
Answer: E
If taxi fares were Rs 1.00 for the first 1/5 mile and Rs 0.20 for each 1/5 miles thereafter. The taxi fare for a 3-mile ride was Choose the most appropriate option:
A) Rs 1.56 B) Rs 2.40 C) RS 3.00 D) Rs 3.80 E) Rs 4.20

Solution: first 1/5 mile costs = 1.00   remaining miles to be covered = 3-1/5 =14/5, =1/5 +1/5+1/5+.... until 14,   hence 14*0.20= 
14*0.20 = 2.8
2.80   total fare= 2.80 + 1.00= 
2.80 + 1.00 = 3.8
3.80   ANSWER:Rs 3.80
Answer: D
A man has some hens and cows. If the number of heads be 48 and the number of feet equals 136, then the number of hens will be Pick one:
A) 22 B) 24 C) 26 D) 20 E) 28

Solution: 28xplanation :   Let number of hens = h and number of cows = c   number of heads = 48   => h + c = 48 ---(28quation 1)   number of feet = 136   => 2h + 4c = 136   => h + 2c = 68 ---(28quation 2)   (28quation 2) - (28quation 1) gives   2c - c = 68 - 48   => c = 20   Substituting the value of c in 28quation 1, we get   h + 20 = 48   => h = 48 - 20= 
48 - 20 = 28
28   i.e., number of hens= 28   Answer : 28
Answer: E
Which of the following equations has a solution in common with x^2 + 14x + 33 = 0?  Choose the correct choice from the following answers:
A) 3x^2 - 5x - 2 = 0  B) -x^2 - 3x + 28 = 0  C) -x^2 - 2x + 99 = 0  D) 3x^2 + 30x + 27 = 0  E) none of the above

Solution: Given : x^2 + 14x + 33 = 0 => (x+3) (x+11) = 0 => -3 and -11 are the roots..   A. 3x^2 - 5x - 2 = 0 => (x-2) (3x+1)   B. -x^2 - 3x + 28 = 0 => (-x+7) (x+4)   C. -x^2 - 2x + 99 = 0 => (x+11) (-x+9)   D. 3x^2 + 30x + 27 = 0 => (x+9) (3x+3)   None of the answer equations have exactly both the same roots as the question equation, but at least one of them does share one of the two roots.   So IMO "C" is correct answer... because it shares the one root (part of the solution), (-11), from the (x+11) portion of its simplification.
Answer: C
The Q train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the Q train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m?
Select the correct option:
A) 1.8m B) 6m C) 7m D) 9m E) 12m

Solution: The reason it is failing for you is that you chose incorrect numbers. If the question says it Q took 7 hrs to reach from A to B and 5 hrs to reach from B to C at a constant speed. It shows that distance AB and BC should be in ratio of 7/5.   If you take such numbers you can solve problem.   A6m = 7, 6mC=5   Therefore   A6m-6mC = 2   6mut from question, A6m-6mC =m   => m=2   Now total distance = A6m+6mC= 12   Substitute 12 to get answer in terms of m   Total distance 6 +6= 
6 +6 = 12
12   Substitute 12 to get answer in terms of m   Total distance=12 =6m   Ans 6m
Answer: B