mathewhe/aqua_rat huggingface dataset:
Question: Certain stocks in April were 10% less than they were in May and 20% Lesser than they were in June. What was the percentage decrease in the stocks from May to June?
(A) 5%
(B) 10%
(C) 20%
(D) 28%
(E) 50%
Rationale: Let stocks value in Feb = 100 => In Jan = 90 and March = 90 * 80/100 = 72
Thus, percent decrease in stocks from Feb to March = 100 - 72 = 28%
Hence Answer is D
Answer: (D) 28%
Question: Lottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 1 on it?
(A) 9/100
(B) 1/10
(C) 11/100
(D) 19/100
(E) 1/5
Rationale: Probability = No of balls with 1 / total number of balls
= {1,10,11,12 to 19, 21,31,41,51,61,71,81,91,100}/100
= 20/100=1/5
Answer is E
Answer: (E) 1/5
Question: find the remainder (32)^33^34 when divided by 11?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: unit digit of 33^34 = 9 i.e odd no.
(32)^33^34 / 11
= (11*3-1)^(-------9) / 11
= (-1)^(odd) / 11
= -1/10
=> rem = -1+11 = 10
ANSWER:B
Answer: (B) 10
Question: 4 + 4 + 4 + 4 + 3 x 4^2 + 3 x 4^3 + 3 x 4^4 + 3 x 4^5 + 3 x 4^6 =
(A)  4^24
(B)  4^20
(C)  4^16
(D)  4^12
(E)  4^7
Rationale: Let's see that 4 + 4 + 4 +4 is 4^2, then: 4^2 + 3 x 4^2 becomes 4 x 4^2 that is 4^3. You follow with the next element: 4^3 + 3 x 4^3 is equal to 4 x 4^3 that is 4^4. Then is assumed right before 3 x 4^6: 4^6 + 3 x 4^6 becomes 4 x 4^6 that is 4^7. Thus, the correct answer is the option E, 4^7.
Answer: (E)  4^7
Question: Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.961. Find the cost of each ice-cream cup?
(A) 25
(B) 66
(C) 77
(D) 99
(E) 91
Rationale: Let the cost of each ice-cream cup be Rs.x
16(6) + 5(45) + 7(70) + 6(x) = 961
96 + 225 + 490 + 6x = 961
6x = 150 => x = 25.
Answer: A
Answer: (A) 25
Question: In Town X, 64 percent of the population are employed, and 40 percent of the population are employed males. What percent of the employed people in Town X are females?
(A) 16%
(B) 24%
(C) 38%
(D) 40%
(E) 52%
Rationale: We are asked to find the percentage of females in employed people.
Total employed people 64%, out of which 40 are employed males,hence 24% are employed females.
(employed females)/(total employed people)=24/64=38%
Answer: C.
Answer: (C) 38%
Question: A boat can move upstream at 35 kmph and downstream at 75 kmph, then the speed of the current is?
A. 5 kmph
(A) 15
(B) 12
(C) 17
(D) 13
(E) 20
Rationale: US = 35
DS = 75
M = (75- 35)/2
= 20
Answer:E
Answer: (E) 20
Question: What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number?
(A) 126
(B) 1386
(C) 3108
(D) 308
(E) 13986
Rationale: There can be 27 numbers. Every digit has three possibilities because question permits repetition. So it becomes a very good summation problem.
If there are 27 digits. There are 27 hundred digits, 27 tens digit and 27 ones digit to be summed. Of 27 hundred digits, 9 of them are 1, 9 of them are 5 and the last 9 are 8. Same is true for the other two digits.
Thus the sum is:
9x100+9x500+9x800+9x10+9x50+9x80+9x1+9x5+9x8=
999x(1+5+8)=999x14=13986
E
Answer: (E) 13986
Question: Sunil invested $ 1800 fir 4 years and $ 1300 for 2 years at the same rate of Simple Interest. If the total interest from these investments is $ 1900, what is the rate of interest?
(A) 18 3/4%
(B) 5 1/3%
(C) 19 1/4%
(D) 16%
(E) 18 2/4%
Rationale: (1800x4xR)/100+(1300x2xR)/100=1900
98R=1900
R= 19 1/4%
Answer is C
Answer: (C) 19 1/4%
Question: Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2178?
(A) 2277
(B) 2669
(C) 2200
(D) 2766
(E) 2998
Rationale: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178.
=> (90%) of (110%) of x = Rs. 2178.
=> (90/100)(110/100)x = 2178
=> x = (2178 * 100)/(9 * 11)
=> x = Rs. 2200
Answer: C
Answer: (C) 2200
Question: Pipe A fills a tank in 42 minutes. Pipe B can fill the same tank 6 times as fast as pipe A. If both the pipes are kept open when the tank is empty, how many minutes will it take to fill the tank?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: A's rate is 1/42 and B's rate is 1/7.
The combined rate is 1/42 + 1/7 = 1/6
The pipes will fill the tank in 6 minutes.
The answer is D.
Answer: (D) 6
Question: A large box contains 18 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box?
(A) 230
(B) 320
(C) 450
(D) 540
(E) 110
Rationale: The number of chocolate bars is equal to
18 *25 = 450
correct answer C
Answer: (C) 450
Question: A small water pump would take 3 hours to fill an empty tank. A larger pump would take 1/4 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?
(A) 3/13
(B) 1/5
(C) 1/10
(D) 1/3
(E) 1/7
Rationale: Rate of the small pump is 1/3 tank/hour
Rate of the larger pump is 1/(1/4) or 4 tank/hour;
Combined rate of the two pumps is 1/3+4=13/3 tank/hour, together they will fill the empty tank in 1/(13/3)= 3/13 hours (time=job/rate).
Answer: A
Answer: (A) 3/13
Question: Susan, John, Tim, Matt and Kim need to be seated in 5 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
(A) A)60
(B) B)120
(C) C)80
(D) D)240
(E) E)60
Rationale: Total number of arrangements = 5! = 120
In exactly half, Susan will be to the left of Tim, which gives us 60 arrangements
Option (A)
Answer: (A) A)60
Question: On the xy co-ordinate plane, point C is (4,-2) and point D is (-1,2.5). The point on line segment CD that is twice as far from C as from D is:
(A) (1,-1)
(B) (1,1)
(C) (2,0.25)
(D) (3,0.5)
(E) (3,1)
Rationale: We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.
*It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:
Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)| = 6
The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is 5-4 = 1, or (-1)+2 = 1.
Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5| = 4.5
The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is (-2)+3 = 1, or 2.5-1.5 = 1.
So now we have our coordinates of the point on the line that is twice as far from C as it is from D: (3,1)
Answer: E
Answer: (E) (3,1)
Question: A man two flats for $675958 each. On one he gains 14% while on the other he loses 14%. How much does he gain or lose in the whole transaction?
(A) 1.96%
(B) 2.56%
(C) 3.12%
(D) 4.65%
(E) 5.12%
Rationale: In such a case there is always a loss
Loss% = (14/10)^2 = 49/25 = 1.96%
Answer is A
Answer: (A) 1.96%
Question: James can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
(A) 365/784
(B) 415/784
(C) 175/256
(D) 256/175
(E) 263/541
Rationale: James will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾
Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256
The probability that he will hit the target at least in one of the four shots=1-81/256
=175/256
Ans: C
Answer: (C) 175/256
Question: If 10 people contributed a total of $30.00 toward a gift and each of them contributed at least $2.00, then the maximum possible amount any one person could have contributed is
(A)  $1.00
(B)  $1.25
(C)  $12.00
(D)  $6.00
(E)  $20.00
Rationale: C for me
9 people with 2$ each -> maximum = 12
Answer: (C)  $12.00
Question: The speed of a bus increases by 2 kmph after every one hour. If the distance travelled in the first one hour was 35 km, what was the total distance travelled in 12 hours?
(A) 550
(B) 500
(C) 552
(D) 560
(E) 580
Rationale: Dist 1st hr = 35 km
speed of bus by 2 kmph 2nd hr = 37 km
3rd hr = 39 km
tot = 35+37+39+....(12 terms)
12/2(2*35+(12-1)2]
=6*92
= 552
ANSWER C
Answer: (C) 552
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $25. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
(A) 9/(25xy)
(B) xy/225
(C) 225/(xy)
(D) 225xy
(E) 25xy/9
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 25 / (xy/9) = 225/(xy).
The answer is C.
Answer: (C) 225/(xy)
Question: How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together?
(A) 9
(B) 15
(C) 32
(D) 56
(E) 72
Rationale: Sol. The given word contains 5 different letters.
Taking the vowels EA together, we treat them as one letter.
Then, the letters to be arranged are XTR (EA).
These letters can be arranged in 4! = 24 ways.
The vowels EA may be arranged amongst themselves in 2! = 2 ways.
Number of words, each having vowels together = (24x2) = 48 ways.
Total number of words formed by using all the letters of the given words
= 5! = (5x4x3x2x1) = 120.
Number of words, each having vowels never together = (120-48) = 72.
Ans: E
Answer: (E) 72
Question: The probability that B can shoot a target two out of two times is 0.5. What is the probability that the target will be missed by B immediately after such two shots?
(A) 0.25
(B) 0.5
(C) 0.75
(D) 0.4
(E) 0.8
Rationale: Suppose there are total 'x' shots.
B shoots 2 out of 2 times. means out of x shots (x>2) B shots 2 out of 2 ----> B shots at least 2 out of x.
therefore, 2/x = 0.5 (given)
the target will be missed by B immediately after such two shots : this means he can shot just twice ...the third shot cannot happen which means he missed (x-2) shots.
thus, the probabilty of missing just after 2 shots is (x-2)/x.
(x-2)/x = 1 - 2/x
= 1 - 0.5
= 0.5
Answer : B
Answer: (B) 0.5
Question: In the x-y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 12 is
(A) 8
(B) 12
(C) 16
(D) 1296
(E) 24
Rationale: I've never seen such kind of question in GMAT before.
OK there can be 4 cases:
|x+y| + |x-y| = 12
A. x+y+x-y = 12 --> x=6
B. x+y-x+y = 12 --> y=6
C. -x-y +x-y= 12 --> y=-6
D. -x-y-x+y=12 --> x=-6
The area bounded by 4 graphs x=6, x=-6, y=6, y=-6 will be square with the side of 4 so the area will be 36*36=1296
Answer:D
Answer: (D) 1296
Question: In how many ways, a committee of 5 members can be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies?
(A) 200
(B) 120
(C) 245
(D) 320
(E) 147
Rationale: (3 men out 6) and (2 ladies out of 5) are to be chosen.
Required number of ways = (6c3x5c2)
= [6x5x4/3x2x1] x [5x4/2x1] = 200.
Ans: A
Answer: (A) 200
Question: Statements: Government has spoiled many top ranking financial institutions by appointing bureaucrats as Directors of these institutions. Assumptions: 1) Government should appoint Directors of the financial institutes taking into consideration the expertise of the person in the area of finance. 2) The Director of the financial institute should have expertise commensurate with the financial work carried out by the institute.
(A) Only conclusion I follows
(B) Only conclusion II follows
(C) Either I or II follows
(D) Neither I nor II follows
(E) Both I and II follow
Rationale: According to the statement, Government has spoiled financial institutions by appointing bureaucrats as Directors. This means that only those persons should be appointed as Directors who are experts in finance and are acquainted with the financial work of the institute. So, both I and II follow.
E
Answer: (E) Both I and II follow
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
(A) 12 sec
(B) 3 sec
(C) 4 sec
(D) 10 sec
(E) 5 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (45 + 72)*5/18 = 32.5 mps.
The time required = d/s = 100/32.5 = 3 sec.
ANSWER:B
Answer: (B) 3 sec
Question: At a particular pizza shop, a pizza can be created from any combination of 7 different types of spice, 7 different types of meat, among which are pepperoni and anchovies, and 4 different types of cheese. If a customer at the shop decides to order a pizza with 1 type of spice, 2 types of cheese, and 4 types of meat but without pepperoni and anchovies together, how many possible ways to garnish the pizza are available to the customer?
(A) 6
(B) 35
(C) 120
(D) 450
(E) 1050
Rationale: Number of possible ways to select 1 type of spice = 7c1 = 7
Number of possible ways to select 2 types of cheese = 4c2 = 6
Number of possible ways to select 4 types of meat but without pepperoni and anchovies together
= Total number of ways without any restriction - Total number of ways in which pepperoni and anchovies together
= 7c4 - 5c2
=35 - 10
=25
Possible ways to garnish the pizza are available to the customer = 7*6 * 25
=1050
Answer E
Answer: (E) 1050
Question: If a and b are positive integers such that a/b = 3.98, which of the following must be a divisor of a?
(A) 67
(B) 197
(C) 91
(D) 199
(E) 42
Rationale: 1) A and B are positive INTEGERS
2) A/B = 3.98
A = 398
B = 100
398/100 = 3.98
These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...
A = 199
B = 50
199/50 = 2.86
There is no other way to reduce this fraction, so A must be a multiple of 199 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 199, we have to 'factor-down' 199. This gives us only (199), excluding 1 itself. So this number MUST be a factor of A. You'll find the match in the answer choices.
Answer: D
Answer: (D) 199
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
(A) 180 m
(B) 1870 m
(C) 050 m
(D) 150 m
(E) 110 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer:D
Answer: (D) 150 m
Question: 50 is divided into two parts such that the sum of their reciprocals is 1/ 12.Find the two parts.
(A) 27 and 23
(B) 25 and 25
(C) 10 and 40
(D) 35 and 15
(E) 30 and 20
Rationale: Let the two parts be x and (50 - x).
Then, 1 / x + 1 / (50 – x) = 1 / 12 => (50 – x + x) / x ( 50 – x) = 1 / 12
=> x2 – 50x + 600 = 0 => (x – 30) ( x – 20) = 0 => x = 30 or x = 20.
So, the parts are 30 and 20.
Answer is E.
Answer: (E) 30 and 20
Question: Calculate the amount that an investor needs to be invest to earn $1023 in interest in 24 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 12% compounded semi-annually?
(A) 3980
(B) 3600
(C) 3700
(D) 3800
(E) 3900
Rationale: the approach is substitution,
our interest requirement is $1023 after 24 months, 2 compounding period.
calculate the compound interest on each option and find out the one that yields $1023 in 24 months
3900 yielded $1023
using the formula
A = P(1 + r/n)nt
hence answer is E
Answer: (E) 3900
Question: here's an easy question of averages, but let's try to see innovative ways of solving this.
A class has 12 boys and x girls. Average score of boys and girls is 80 and 92 respectively. the average of the whole class is 86, what is the value of x?
(A) a) 6
(B) b) 7
(C) c) 8
(D) d) 10
(E) e) 12
Rationale: 12(80)+92x/12+x=86
960+92x/12+x=86
960+92x=86(12+x)
960+92x=1032+86x
X's one side, numbers one side we get,
92x - 86x=1032-960
6x=72
hence, x=12
Answer E
Answer: (E) e) 12
Question: Ranjit went to the market with Rs. 100. If he buys 3 pens and 6 pencils he uses up all his money. On the other hand, if he buys 3 pencils and 6 pens he would fall short by 20%. If he wants to buy equal number of pens and pencils, how many pencils can he buy?
(A) 222
(B) 277
(C) 267
(D) 100
(E) 221
Rationale: Let price of a pen = x and pencil = y
3x + 6y = 100 ....(i)
and 6x + 3y = 125 ....(ii)
Adding (i) and (ii)
9(x + y) = 225
x + y = 25
multiply by 4
4x + 4y = 100
He can by 4 pens and 4 pencils in Rs. 100.
Answer:D
Answer: (D) 100
Question: A movie buff buys movies on DVD and on Blu-ray in a ratio of 13:4. If she returns 2 Blu-ray movies, that ratio would change to 7:2. If she buys movies on no other medium, what was the original number of movies purchased?
(A) 22
(B) 28
(C) 77
(D) 99
(E) 119
Rationale: Now coming to the process m(D) = 13x and b(D) = 4x
now from the next line the new eqn becomes 13x/ (4x -2) = 7/2
Solving it 26x = 28x -14
x =7
which means m (d) = 91 and b(d) = 28
SO total initially is m(d) + b(d) = 119
E
Answer: (E) 119
Question: On a test, 15% of the students received an A, 60% of the remaining students received a below a B. What percentage of the students received a B?
(A) 15% of the students received a B.
(B) 60% of the students received a B.
(C) 51% of the students received a B.
(D) 66% of the students received a B.
(E) None of these.
Rationale: Explanation:Let total number of students be 100,Then, number of students who received an A = 15.Number of students receiving below a B = 60% of 85 = 51.Total number of students arriving alone = 100 – (15 + 51) = 34.Thus, 34% of the students received a B.Answer: Option E.
Answer: (E) None of these.
Question: John tossed a fair coin 4 times. What is the probability that the coin landed heads up exactly twice?
(A) 0.15
(B) 0.25
(C) 0.3
(D) 0.35
(E) 0.4
Rationale: The probability is exactly same as the cion landed tail up once. That is 4*(1/2)^4 = 4/16 =0.25.
The answer is, therefore, (B).
Answer: (B) 0.25
Question: A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?
(A) 2777
(B) 2565
(C) 9877
(D) 1900
(E) 1557
Rationale: 2000 ---- 54
2000 ---- 39
x ----- 20
x*20 = 2000*39
x = 3900
2000
-------
1900
Answer:D
Answer: (D) 1900
Question: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections E of the 4 items can Amanda make?
(A) 9
(B) 12
(C) 14
(D) 15
(E) 60
Rationale: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?
3! / 1!2! * 6! / 3!3!
E=3*20=60
E. 60
Answer: (E) 60
Question: Which of the following equations is NOT equivalent to 4a^2 = b^2 - 9 ?
(A)  4a^2 + 9 = b^2
(B)  4a^2 - b^2 = -9
(C)  4a^2= (b + 3)(b - 3)
(D)  2a = b - 3
(E) a^2 = (b^2-9)/4
Rationale: 4a^2 = b^2 - 9
The basic rule when dealing with equations is that you can do ANYTHING to both sides of an equation as long as you do it EQUALLY to BOTH sides. Everything gets a bit more complex when you're dealing with variables in the denominator of a fraction and/or inequalities, but neither of those subjects is a factor in this prompt.
Looking at Answer D, we have....
2a = b - 3
While you COULD take the square root of both sides of the original equation, it's important to note that the square root of b^2 - 9 is NOT (b-3).
b^2 - 9 can be factored into (b-3)(b+3), but neither of these parentheses is the square root of b^2 - 9.
You can see the proof when you square either of the two parentheses:
(b-3)^2 = b^2 - 6a + 9
(b+3)^2 = Y^2 + 6a + 9
Thus, D is NOT equivalent to the prompt.
Answer: (D)  2a = b - 3
Question: A basketball player succeeds with 70% of her free throws. If she has a set of three free throws, what is the probability that she succeeds at least once?
(A) 0.952
(B) 0.964
(C) 0.973
(D) 0.985
(E) 0.992
Rationale: P(missing all 3 free throws) = 0.3^3 = 0.027
P(succeeding at least once) = 1 - 0.027 = 0.973
The answer is C.
Answer: (C) 0.973
Question: A car takes 8 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 10Kmph
(B) 45Kmph
(C) 60Kmph
(D) 55Kmph
(E) 30Kmph
Rationale: Time = 8
Distence = 540
3/2 of 8 hours = 8 * 3/2 = 12 Hours
Required speed = 540/12 = 45 Kmph
B)
Answer: (B) 45Kmph
Question: Two pipes A and B can separately fill a tank in 12 and 15 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?
(A) 590 liters
(B) 540 liters
(C) 740 liters
(D) 560 liters
(E) 580 liters
Rationale: 1/12 + 1/15 - 1/x
= 1/15
x = 12
12 * 45 = 540
Answer:B
Answer: (B) 540 liters
Question: A sum of money invested at C.I. amounts to Rs. 800 in 3 years to Rs. 850 in 4 years. The rate of interest per annum is?
(A) 2 1/2 %
(B) 4%
(C) 5%
(D) 6 2/3 %
(E) 6 1/4%
Rationale: S.I. on Rs. 800 for 1 year = (850 - 800) = Rs. 50 Rate = (100 * 50)/(800 * 1) = 6 1/4%
ANSWER:E
Answer: (E) 6 1/4%
Question: There are 133 employees in Company X. If the number of employees who birth in June is the greatest, what is the least possible number of the employees in the company who birth in June?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: IMO 12
Take each answer choice and substract it from 133 and the divided this with 11.
B
Answer: (B) 11
Question: L9Q,L36S,P81U,R144W,T225U,?
(A) V434Y
(B) U475Y
(C) V472Z
(D) V324Y
(E) V361X
Rationale: L + Q = 9
L + S = 36
P + U = 81
R + W = 144
T + W = 225
3^2 , (3*2=6)^2 , (3*3)^2 , (3*4)^2 , (3*5)^2 ---> AS per this number sequence
=> next number = (3*6)^2 = 324
V + Y =324 => V324Y
ANSWER:D
Answer: (D) V324Y
Question: What is the place value of 7 in the numeral 7259
(A) A)2700
(B) B)2800
(C) C)2900
(D) D)7000
(E) E)3000
Rationale: 7 * 1000 = 7000
D
Answer: (D) D)7000
Question: Which is the least number that must be subtracted from 1856 so that the remainder when divided by 7, 12, 10 is 4?
(A) 168
(B) 172
(C) 182
(D) 140
(E) 160
Rationale: First we need to figure out what numbers are exactly divisible by 7,12,10. This will be the set {LCM,LCMx2,LCMx3,...}
LCM(7,12,10) = 42*10 = 420
The numbers which will leave remainder 4 will be {420+4, 420x2 +4, ,...}
The largest such number less than or equal to 1856 is 420*4+4 or 1684
To obtain this you need to subtract 172.
B
Answer: (B) 172
Question: A train 150 m long running at 72 kmph crosses a platform in 20 sec. What is the length of the platform?
(A) 443 m
(B) 354 m
(C) 450 m
(D) 350 m
(E) 250 m
Rationale: E
250
E = 72 * 5/18 = 20 = 400 â€“ 150 = 250
Answer: (E) 250 m