mathewhe/aqua_rat huggingface dataset:
Question: In the xy-coordinate plane, the graph of y = -x^2 + 9 intersects line L at (p,5) and (t,7). What is the least possible value of the slope of line L?
(A) 6
(B) 2
(C) -2
(D) 1
(E) -10
Rationale: We need to find out the value of p and L to get to the slope.
Line L and Graph y intersect at point (p,5). hence, x= p and Y=5 should sactisfy the graph. soliving
5 = -p2 +9
p2 = 4
p = + or - 2
simillarly point (t,7) should satisfy the equation. hence x=t and Y=7.
-7 = -t2+9
t = +or - 4
considering p = -2 and t =4, the least slope is (7-5)/(4-2) = 1
IMO option D is correct answer.
Answer: (D) 1
Question: A wheel of a car of radius 21 cms is rotating at 800 RPM. What is the speed of the car in km/hr?
(A) 79.2 km/hr
(B) 47.52 km/hr
(C) 7.92 km/hr
(D) 39.6 km/hr
(E) 63.36 km/hr
Rationale: Explanatory Answer
The radius of the wheel measures 21 cm.
In one rotation, the wheel will cover a distance which is equal to the circumference of the wheel.
∴ in one rotation this wheel will cover 2 * π * 21 = 132 cm.
In a minute, the distance covered by the wheel = circumference of the wheel * rpm
∴ this wheel will cover a distance of 132 * 800 = 105600 cm in a minute.
In an hour, the wheel will cover a distance of 105600 * 60 = 6336000 cm.
Therefore, the speed of the car = 6336000 cm/hr = 63.36 km/hr
Choice E is the correct answer.
Answer: (E) 63.36 km/hr
Question: {330, 380, 350, n}
Which of the following could be the median of the 4 integers listed above?
I. 340
II. 360
III. 380
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
Rationale: If 340 is the median, (n+350) / 2 = 340. Then n = 330. Thus 340 can be the median.
If 360 is the median, (n+350) / 2 = 360. Then n = 370. Thus 360 can be the median.
If 380 is the median, (n+350) / 2 = 380. Then n = 410. But 410 > 380, which would then be the second largest member of the set, thus 380 can not be the median.
The answer is C.
Answer: (C) I and II only
Question: A certain team has 11 members, including Joey. A three-member relay team will be selected as follows: one of the 11 members is to be chosen at random to run first, one of the remaining 10 members is to be chosen at random to run second, and one of the remaining 9 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?
(A) 1/1320
(B) 1/132
(C) 2/11
(D) 1/12
(E) 1/6
Rationale: Total outcomes= 11*10*9
Favorable Outcomes= 10*1*9 and 10*9*1
P=2*10*9*1/11*10*9
P=2/11
Ans C
Answer: (C) 2/11
Question: A sum of Rs.5000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
(A) A)282
(B) B)3250
(C) C)8383
(D) D)8383
(E) E)3284
Rationale: Let A be the amount received at the end of the three years.
A = 5000[1 + 10/100][1 + 20/100][1 + 25/100]
A = 5000 * 1.65
A = Rs.8250
So the interest = 8250 - 5000 = Rs.3250
Answer: B
Answer: (B) B)3250
Question: s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits T are in s(99)?
(A) T=350
(B) T=353
(C) T=354
(D) T=356
(E) 357
Rationale: Focus on the points where the number of digits in squares change:
1, 2, 3 - Single digit squares. First 2 digit number is 10.
4 , 5,...9 - Two digit squares. To get 9, the last number with two digit square, think that first 3 digit number is 100 which is 10^2. so 9^2 must be the last 2 digit square.
10, 11, 12, ... 31 - Three digit squares. To get 31, think of 1000 - the first 4 digit number. It is not a perfect square but 900 is 30^2. 32^2 = 2^10 = 1024, the first 4 digit square.
32 - 99 - Four digit squares. To get 99, think of 10,000 - the first 5 digit number which is 100^2.
So number of digits in s(99) = 3*1 + 6*2 + 22*3 + 68*4 = 3 + 12 + 66 + 272 = 353.B
Answer: (B) T=353
Question: A, B, and C working alone can finish constructing a house in 6, 9, and 12 hours respectively. A starts alone and works for 1 hour. He is then joined by B and they work together for 1 hour. Finally C joins them and they all work together to finish the work. If they start working at 9 am, at what time will they finish?
(A) 11:38 am
(B) 11:49 am
(C) 12:11 pm
(D) 12:32 pm
(E) 12:43 pm
Rationale: A completes 1/6 of the job each hour.
B completes 1/9 of the work each hour.
C completes 1/12 of the work each hour.
A completes 1/6 of the work in the first hour.
Working together, A and B complete another 5/18 for a total of 8/18.
Working together, A, B, and C can complete 13/36 of the work each hour.
To complete 20/36, the time required is (20/36) / (13/36) = 20/13 hours.
The work will be completed at 12:00 plus 7*60/13 minutes which is about 12:32 pm.
The answer is D.
Answer: (D) 12:32 pm
Question: It costs $5 for the first 1/3 hour to use the laundry machine at the Laundromat. After the first ¼ hour it costs $12 per hour. If a certain customer uses the laundry machine for 2 hours and 30 minutes, how much will it cost him?
(A) $27.
(B) $29.
(C) $31.
(D) $33.
(E) $35.
Rationale: 2 hrs 30 min = 150 min
First 20 min ------> $5
Time left is 130 min...
Now, 60 min costs $ 12
1 min costs $ 12/60
150 min costs $ 12/60*130 => $ 26.00
So, Total cost will be $26 + $5 => $ 31
Hence answer will be C
Answer: (C) $31.
Question: The C.P of 10 pens is equal to the S.P of 13 pens. Find his gain % or loss%?
(A) loss 16 2/8%
(B) loss 16 6/3%
(C) loss 23.08%
(D) loss 18 2/3%
(E) loss 16 25%
Rationale: 10 CP = 13 SP
13 --- 3 CP loss
100 --- ? => 23.08% loss
Answer:C
Answer: (C) loss 23.08%
Question: A boat moves upstream at the rate of 1 km in 40 minutes and down stream 1 km in 12 minutes. Then the speed of the current is :
(A) 1 kmph
(B) 2 kmph
(C) 1.75 kmph
(D) 2.5 kmph
(E) 3.5 kmph
Rationale: Rate upstream = (1/40 *60) = 1.5 kmph
Rate dowm stream = 1/12 * 60 = 5 kmph
Rate of the current = ½ (5-1.5) = 1.75 kmph
ANSWER:C
Answer: (C) 1.75 kmph
Question: For all real numbers v, an operation is defined by the equation v* = v - v/3. If (v*)* = 12, then v=
(A) 15
(B) 18
(C) 21
(D) 24
(E) 27
Rationale: (v*)* = (v - v/3) - (v - v/3) / 3
12 = 2v/3 - 2v/9 = 4v/9
v = 27
The answer is E.
Answer: (E) 27
Question: Lucia's sells kale at x dollar per pound for the first 20 pounds and .8x for every subsequent pound. Amby's price is x per pound for the first 14 pounds and .9x for subsequent pounds. What is the minimum number of pounds over 15 for which Lucia's becomes an equal or better deal?
(A) 24
(B) 26
(C) 25
(D) 27
(E) 28
Rationale: For Amy's deal to be better, the cost has to be less or equal to Lucia's
Assuming 'n' is the number of pounds of kale, the equation is
20x + (n-20) (0.8x) <= 14x + (n-14)(0.9x)
Resolve it:
==> 20x + 0.8nx - 16x <= 14x + 0.9nx - 12.6x
==> 2.6x <=0.1nx
==> 26x < =nx
==> x (n-26) > = 0
as x cannot be 0,
==> n - 26 >=0
==> n > = 26
so the minimum value is 26
'B' would be the correct answer
Answer: (B) 26
Question: The average weight of 8 students decreases by 5 kg when one of them weighing 86 kg is replaced by a new student. The weight of the student is
(A) 46 kg
(B) 48 kg
(C) 70 kg
(D) 72 kg
(E) None of these
Rationale: Explanation :
Let the weight of student be x kg.
Given, Difference in average weight = 5 kg
=> (86-x)/8 = 5
=> x = 46
Answer : A
Answer: (A) 46 kg
Question: If x = -1/8 and y = -1/2, what is the value of the expression -2x – y^2?
(A) -3/2
(B) -1
(C) 0
(D) 3/2
(E) 7/4
Rationale: -2X- y^2
-2x-1/8 - (-1/2)^2
1/4-1/4
0
C correct
Answer: (C) 0
Question: To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of L dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?
(A) L/T
(B) L/(T-S)
(C) SL/(T-S)
(D) SL/T(T-S)
(E) L(T-S)/T
Rationale: Since no absolute values are given in the question we can replace the given parameters with assumed numbers,
Let Total colleagues be 100 (T)
Let total contribution be 1000 (L) (point to note is that its total cost not per person)
Those who dont pay are S (30)
Per person cost = L/T = 1000/100 = 10
So cost for those who failed to pay = (L/T) * S = SL/T = 30*10=300
The equation for people who would bear the total cost after S people fail = (T-S)=70
There fore the solution is (SL/T)/ (T-S) = SL/T(T-S) = 300/70
Answer D
Hope this helps !!!
Answer: (D) SL/T(T-S)
Question: 18 times a positive integer is more than its square by 80, then the positive integer is
(A) 13
(B) 10
(C) 11
(D) 12
(E) 14
Rationale: Explanation:
Let the number be x. Then,
18x = x2 + 80
=> x2 - 18x + 80 = 0
=>(x - 10)(x - 8) = 0
=> x = 10 or 8
Answer: B
Answer: (B) 10
Question: At 1:00 pm, there were 10.0 grams of bacteria. The bacteria increased to x grams at 4:00 pm, and 25.6 grams at 7:00 pm. If the amount of bacteria present increased by the same fraction during each of the 3-hour periods, how many grams of bacteria were present at 4:00 pm?
(A) 15.1
(B) 15.4
(C) 15.7
(D) 16.0
(E) 16.3
Rationale: Let x be the factor by which the bacteria increases every three hours.
At 4:00 pm, the amount of bacteria was 10x and at 7:00 pm it was 10x^2.
10x^2 = 25.6
x^2=2.56
x=1.6
At 4:00 pm, the amount of bacteria was 10(1.6)=16 grams.
The answer is D.
Answer: (D) 16.0
Question: The size of the wooden block is 5 x 10 x 20 cm .How many such blocks will be required to construct a solid wooden cube of minimum size?
(A) 6
(B) 8
(C) 12
(D) 16
(E) 18
Rationale: Explanation:
Side of smallest cube = L.C.M of 5,10,20 = 20cm
Volume of the cube = (20 x 20 x 20)cm3 = 8000 cm3
Volume of the block= (5 x 10 x 20) cm3 = 1000 cm3
Number of blocks = (8000/1000) = 8
Answer: B
Answer: (B) 8
Question: If the number 653 xy is divisible by 90, then (x + y) = ?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 5
Rationale: 90 = 10 x 9
Clearly, 653xy is divisible by 10, so y = 0
Now, 653x0 is divisible by 9.
So, (6 + 5 + 3 + x + 0) = (14 + x) is divisible by 9. So, x = 4.
Hence, (x + y) = (4 + 0) = 4.
Answer: C
Answer: (C) 4
Question: What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052,3158, x
(A) 2643
(B) 5464
(C) 9476
(D) 7554
(E) 3158
Rationale: 12
12 Ã— 3 + 2 = 38
38 Ã— 3 + 2 = 116
116 Ã— 3 + 2 = 350
350 Ã— 3 + 2 = 1052
11052 Ã— 3 + 2 = 3158
3158 Ã— 3 + 2 = 9476
C
Answer: (C) 9476
Question: A and B enter into partnership with capitals in the ratio 3 : 4. At the end of 10 months A withdraws,and the profits now are divided in the ratio of 3 : 2. Find how long B remained in the business?
(A) 5 months
(B) 8 months
(C) 6 months
(D) 7 months
(E) None of these
Rationale: Initially A’s investment = 3x and B’s investment = 4x
Let B remain in the business for ‘n’ months.
⇒ 3x × 10 : 4x × n = 3 : 2
∴ 3x × 10 × 2 = 4x × n × 3
⇒ n = 5
Answer A
Answer: (A) 5 months
Question: An air conditioner can coo the hall in 40 miutes while another takes 45 minutes to cool under similar conditions. if both air conditioners are switched on at same instance then how long will it take to cool the room?
(A) about 22 minutes
(B) about 20 minutes
(C) about 30 minutes
(D) about 25 minutes
(E) about 15 minutes
Rationale: Take LCM of 40 and 45 = 360
40*9=360 / 45*8=360.
So if both are switched on together , room cooled in 360/(8+9)=360/17=21.16 minutes
21.16 can be round to 22 minutes , so about 22 minutes
ANSWER:A
Answer: (A) about 22 minutes
Question: A rope of which a calf is tied is increased from 12 m to 25 m, how much additional grassy ground shall it graze?
(A) 1217
(B) 1219
(C) 1511.7
(D) 1212
(E) 1312
Rationale: π (252 – 122) = 1511.7
Answer:C
Answer: (C) 1511.7
Question: The average temperature of the town in the first four days of a month was 56 degrees. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?
(A) 62 degrees
(B) 64 degrees
(C) 65 degrees
(D) 128 degrees
(E) 67 degrees
Rationale: Explanation:
Sum of temperatures on 1st, 2nd, 3rd and 4th days = (56 * 4) = 224 degrees ... (1)
Sum of temperatures on 2nd, 3rd, 4th and 5th days - (60 * 4) = 240 degrees ....(2)
Subtracting (1) From (2), we get :
Temp, on 5th day - Temp on 1st day = 16 degrees.
Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively.
Then, 8x - 7x = 16 or x = 16. Answer: D
Temperature on the 5th day = 8x = 128 degrees.
Answer: (D) 128 degrees
Question: There was two trains from calcutta to kanyakumari one train is fast service travels with a speed 75km per hour another travels with a speed of 44km per hour the time taken to reach from calcutta to kanyakumari is 4hours less than the first train...find the distance b/w calcatta to kanyakumari
(A) 415.8 km
(B) 425.8 km
(C) 435.8 km
(D) 445.8 km
(E) 455.8 km
Rationale: let distance b/w calcutta to kanyakumari is = x km
then eqn is
x/44 - x/75 = 4
=> x*(75-44)=4*75*44
=> x = 425.8 km
ANSWER:B
Answer: (B) 425.8 km
Question: The arithmetic mean and standard deviation of a certain normal distribution are 16.2 and 2.3, respectively. What value is exactly 2 standard deviations less than the mean?
(A) 10.5
(B) 11
(C) 11.6
(D) 12
(E) 12.5
Rationale: Mean = 16.2
Two standard deviations is 2.3 + 2.3 = 4.6
There could be two calues for this.
Mean + two standard deviations = 20.8
Mean - Two standard deviations = 11.6
Answer choice has 11.6 and so C is the answer.
Answer: (C) 11.6
Question: If 4a = 16b and 9b = 11c, Find a:b:c?
(A) 52:13:7
(B) 44:11:9
(C) 7:13:52
(D) 7:13:54
(E) None of these
Rationale: Explanation:
(4a = 16b ==> a/b = 16/4)
and (9b = 11c ==> b/c = 11/9)
==> a:b = 16:4 and b:c = 11:9
a:b:c = 44:11:9
Answer: Option B
Answer: (B) 44:11:9
Question: A wooden cube whose edge length is 8 inches is composed of smaller cubes with edge lengths of one inch. The outside surface of the large cube is painted red and then it is split up into its smaller cubes. If one cube is randomly selected from the small cubes, what is the probability that the cube will have at least one red face?
(A) 46.3%
(B) 50.4%
(C) 54.2%
(D) 57.8%
(E) 61.3%
Rationale: There are a total of 8*8*8 = 512 cubes.
All the exterior cubes will have at least one face painted red.
The interior is formed by 6*6*6 = 216 cubes.
The number of cubes with at least one side painted red is 512 - 216 = 296 cubes
The probability that a cube has at least one side painted red is 296/512 which is about 57.8%
The answer is D.
Answer: (D) 57.8%
Question: The speed of the boat in still water in 12 kmph. It can travel downstream through 39 kms in 3 hrs. In what time would it cover the same distance upstream?
(A) 3.5 hours
(B) 6 hours
(C) 4 hours
(D) 5 hours
(E) 6 hours
Rationale: Still Water=12km/hr
Downstream=39/3=13km/hr
Upstream=>> still water=(u+v/2) =>> 12=u+13/2 = 11km/hr
So time taken in upstream = 39/11 =3.5hrs
ANSWER:A
Answer: (A) 3.5 hours
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
(A) 11 1/5
(B) 11 1/4
(C) 11 1/5
(D) 11 1/3
(E) 11 2/3
Rationale: 3/12 + x/15 = 1
x= 11 1/4
Answer: B
Answer: (B) 11 1/4
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
(A) 5
(B) 8
(C) 7
(D) 4
(E) 2
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Answer: (B) 8
Question: The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?
(A) 27.5%
(B) 37.5%
(C) 47.5%
(D) 57.5%
(E) 67.5%
Rationale: 100 * 100 = 10000
110 * 125 = 13750
-----------
3750
10000 ------ 3750
100 ------- ? => 37.5%
ANSWER:B
Answer: (B) 37.5%
Question: If a certain sample of data has a mean of 20.0 and a standard deviation of 5.0, which of the following values is more than 2.5 standard deviations from the mean?
(A)  12.0
(B)  13.5
(C)  17.0
(D)  23.5
(E)  26.5
Rationale: The standard deviation is 5. 2.5 standard deviations, which is just 2.5 x 5.0 is 12.5. The only answer more than 12.5 away from the mean is B.
Answer: (B)  13.5
Question: A store’s selling price of $2240 for a certain computer would yield a profit of 40 percent of the store’s cost for the computer. What selling price would yield a profit of 50 percent of the computer’s cost?
(A) $2400
(B) $2464
(C) $2650
(D) $2732
(E) $2800
Rationale: 2240 = X * 1.4 = X * (7/5). Therefore, X = 2240 * 5/7.
2240 is easily divided by 7 to be 320, which is then easily multiplied by 5 to give X = 1600. To get 50% profit, you need 1600 * 1.5 = 2400.
Answer: A
Answer: (A) $2400
Question: The sum of 2 consecutive numbers is definitely:
(A) is odd
(B) Divisible by 2.
(C) Divisible by 3.
(D) Divisible by 4.
(E) Divisible by 5.
Rationale: If 1st term is x:
x+(x+1)=2x+1--->is odd
If 2nd term is x:
(x-1)+x=2x-1 --->is odd
Answer: A
Answer: (A) is odd
Question: A train leaves station X at 5 a.m. and reaches station Y at 9 a.m. Another train leaves station Y at 7 a.m. and reaches station X at 10 : 30 a.m. At what time do the two trains cross each other ?
(A) 7 : 36 am
(B) 7 : 56 am
(C) 8 : 36 am
(D) 8 : 56 am
(E) None of these
Rationale: Let the distance between X and Y be x km. Then,
the speed of A is x⁄4 km/h and that of B is 2x⁄7 km/h.
Relative speeds of the trains
= (x⁄4 + 2x⁄7) = 15x⁄28 km/h
Therefore the distance between the trains at 7 a.m.
= x - x⁄2 = x⁄2 km
Hence, time taken to cross each other
= x/2 /15x/28=x/2×28/15x=14/15×60=56min.
Thus, both of them meet at 7 : 56 a.m.
Answer B
Answer: (B) 7 : 56 am
Question: An article is bought for Rs.575 and sold for Rs.900, find the gain percent?
(A) 73 1/3%
(B) 63 1/3%
(C) 33 1/3%
(D) 93 1/3%
(E) 56.5%
Rationale: Explanation:
575 ---- 325
100 ---- ? => 56.5%
Answer:E
Answer: (E) 56.5%
Question: There are 100 boys in a hostel. Each plays either cricket or softball or both. If 60% play cricket and 50% play softball, how many play both?
(A) 20
(B) 50
(C) 10
(D) 100
(E) 60
Rationale: n(A) = 50*100/100 = 50
n(B) = 60*100/100 = 60
n(AUB) = 100
n(AnB) = 50+60-100 = 10
Answer is C
Answer: (C) 10
Question: How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a consonant and the last letter has to be a consonant, and each letter can be used only once?
(A) 21
(B) 42
(C) 1500
(D) 600
(E) 720
Rationale: Vowel: E O
Consonants: V R M N T
First letter can be filled in 5 Ways ( As the question states that first letter has to be a consonant)
Fifth letter can be filled in 4 Ways ( As the question states that the last letter has to be a consonant)
Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and Fifth letter
Second letter can be filled in 5 Ways
Third letter can be filled in 4 Ways
Fourth letter can be filled in 3 Ways
So, Total number of ways = 5 Ways x 5 Ways x 4 ways x 3 ways x 5 ways = 1500
Answer C
Answer: (C) 1500
Question: A batsman scored 120 runs which included 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets
(A) 30%
(B) 50%
(C) 60%
(D) 80%
(E) 90%
Rationale: Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 120 - (60)
= 60
Now, we need to calculate 60 is what percent of 120.
=> 60/120 * 100 = 50%
B
Answer: (B) 50%
Question: Hyderabad Chennai Mumbai Delhi Bangalore Trivandram ;
Hyderabad
Chennai
Mumbai
Delhi
Bangalore
Trivandram
In the table above, what is the least number of table entries that are needed to show the mileage between each city and each of the other five cities?
(A) 20
(B) 18
(C) 14
(D) 15
(E) 16
Rationale: Easy way to go about this problem is we have 6*6 = 36 enteries in table the least number of enteries would be (36 - 6) /2 since 6 enteries represent the distances between same points .
Alternatively this can be solved as combination problem.
Correct Answer D
Answer: (D) 15
Question: The average age of a group of 20 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
(A) 22 years
(B) 30 years
(C) 42 years
(D) 32 years
(E) None of these
Rationale: Answer
The average age of a group of 20 students is 20.
Therefore, the sum of the ages of all 20 of them = 20 * 20 = 400
When two new students join the group, the average age increases by 2. New average = 22.
Now, there are 22 students.
Therefore, the sum of the ages of all 22 of them = 22 * 22 = 484
Therefore, the sum of the ages of the two new students who joined = 484 - 400 =84
And the average age of each of the two new students = 84/2 = 42 years.
Answer C
Answer: (C) 42 years
Question: A train traveled the first d miles of its journey it an average speed of 40 miles per hour, the next d miles of its journey at an average speed of y miles per hour, and the final d miles of its journey at an average speed of 160 miles per hour. If the train’s average speed over the total distance was 96 miles per hour, what is the value of y?
(A)  68
(B)  84
(C)  100
(D)  120
(E)  135
Rationale: Average speed=Total distance traveled /Total time taken
3d/d/40+d/y+d/160=96
Solving for d and y,
15y=11y+480
4y=400
y=100
Answer C
Answer: (C)  100
Question: When ticket sales began, Pat was the mth customer in line for a ticket, and customers purchased their tickets at the rate of x customers per minute. Of the following, which best approximates the time, in minutes, that Pat had to wait in line from the moment ticket sales began?
(A) (m - 1) x
(B) m + x –1
(C) (m-1)/x
(D) x/(m-1)
(E) m/(x-1)
Rationale: C. (m - 1) / x
Answer: (C) (m-1)/x
Question: Which of the following coordinates are on the line segment connecting (5, 6) and (21, 18)?
(A)  (9, 9)
(B)  (12, 12)
(C)  (13, 13)
(D)  (12, 13)
(E)  (16, 15)
Rationale: The line segment connects (5,6) to (21,18), therefore the change in the x-coordinate is 16, and the change in the y-coordinate is 12. We can simplify that to a slope of 3/4. That is, the points on the line with integer coordinates will all be of the form (5+4n, 6+3n). Put simply, starting at the point (5,6), to find the next point with integer coordinates on the line, all we have to do is add 4 to the x-coordinate and 3 to the y-coordinate. Then we can continue to do that until we find one of the answer choices.
In this case, the next point would be (5+4, 6+3), or (9,9). That is one of the answer choices, so the answer is A.
If (9,9) wasn't an option we could continue to add 4 to the x-coordinate and 3 to the y-coordinate until we found a point that was in the answer choices. The points are:
(5,6)
(9,9)
(13,12)
(17,15)
(21,18)
Beyond that and we are no longer on the line segment connecting the two original points.
Answer: A
Answer: (A)  (9, 9)
Question: Of the 800 employees of Company X, 70 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 40 percent ?
(A) 200
(B) 160
(C) 400
(D) 80
(E) 56
Rationale: The # oflong-termemployees is 70%*800=560.
After y of them retire new # oflong-termemployees would become 560-y.
Total # of employees would become 800-y.
We want 560-y to be 40% of 800-y --> 560-y=(800 -y)*40% --> y = 400.
Answer: C.
Answer: (C) 400
Question: If a = 4p, where p is a prime number greater than 2, how many different positive even divisors does a have, including a ?
(A)  Two
(B)  Three
(C)  Four
(D)  Six
(E)  Eight
Rationale: a=4p
since a = 4p thenevendivisors are:
4p/4p= 1
4p/2p= 2
4p/4= p
4p/2= 2p
so the answer is (C)
Answer: (C)  Four
Question: Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he:
(A) broke even
(B) lost 4 cents
(C) gained 4 cents
(D) lost 10 cents
(E) gained 10 cents
Rationale: 20 % profit on $ 1.20
= $ 20/100 * 1.20
= $ 0.20 * 1.20
= $ 0.24
Similarly, 20 % loss on $ 1.20
= $ 20/100 * 1.20
= $ 0.20 *1.20
= $ 0.24
Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.
Since both profit and loss amount is same so, it’s broke even.
correct answer A
Answer: (A) broke even