mathewhe/aqua_rat huggingface dataset:
Question: The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
(A) 1200
(B) 2400
(C) 4800
(D) Cannot be determined
(E) None
Rationale: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Solve the (ii) and (iii) equations,then will get
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
Option B
Answer: (B) 2400
Question: How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?
(A) 376
(B) 367
(C) 297
(D) 268
(E) 198
Rationale: The smallest number in the series is 1000, a 4-digit number.
The largest number in the series is 4000, the only 4-digit number to start with 4.
The left most digit (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.
The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.
Hence, there are 3 x 5 x 5 x 5 or 375 numbers from 1000 to 3999.
Including 4000, there will be 376 such numbers.
Answer: A
Answer: (A) 376
Question: It costs $2 for the first 1/6 hour to use the laundry machine at the Laundromat. After the first ¼ hour it costs $15 per hour. If a certain customer uses the laundry machine for 2 hours and 25 minutes, how much will it cost him?
(A) $42.25.
(B) $40.25.
(C) $38.25.
(D) $36.25.
(E) $34.25
Rationale: 2 hrs 25 min = 145 min
First 10 min ------> $2
Time left is 135 min...
Now, 60 min costs $ 15
1 min costs $ 15/60
145 min costs $ 15/60*145 => $ 36.25
So, Total cost will be $36.25 + $2 => $ 38.25
Hence answer will be C
Answer: (C) $38.25.
Question: The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 5 times the probability that both events A and B occur. What is the probability that event A occurs?
(A) 1/45
(B) 1/2
(C) 1/8
(D) 2/3
(E) 2/11
Rationale: Let us say probability of A occuring is a.
Let us say probability of B occuring is b.
a = 2b
Probability (either A or B or both) = 5 times Probability (A and B)
a*(1-b) + b*(1-a) + ab = 5*ab
Substituting a=2b in the second equation:
2b*(1-b) + b*(1-2b) + 2b*b = 5*2b*b
3b-2b^2 = 110b^2
3b = 12b^2
b = 3/12 = 1/4
So, a = 2b = 1/2
Answer: (B) 1/2
Question: If A is the set of numbers possible for the eighth term in a sequence of eight consecutive integers that has 6 as its fourth term, which of the following is A?
(A) 2 and 11
(B) 2 and 10
(C) 2 and 9
(D) 3 and 9
(E) 3 and 10
Rationale: First Take 6 as the 4th term from begiining, 8th term will be 10.
Now, take 6 as the 4th last term from the beginning, 8th last term will be 2. Hence B.
Answer: (B) 2 and 10
Question: Today is Monday. After 61 days, it will be
(A) Thursday
(B) Sunday
(C) Monday
(D) Saturday
(E) None of these
Rationale: Explanation :
61 days = 8 weeks 5 days = 5 odd days
Hence if today is Monday, After 61 days, it will be = (Monday + 5 odd days)
= Saturday .Answer : Option D
Answer: (D) Saturday
Question: A project manager needs to select a group of 3 people from a total of 3 men and 3 women. How many possible group combinations exist such that no group has all men ?
(A) 72
(B) 68
(C) 24
(D) 19
(E) 48
Rationale: Since the order in which the group is selected does not matter, we are dealing with a combinations problem (and not a permutations problem).
The formula for combinations is:
N!/((N-K)!K!)
Where N = the total number of elements from which we will select, 6 people in this case.
Where K = the total number of elements to select, 3 people in this case.
The total number of combinations is therefore:
6!/((6-3)!3!) = 20
However, one of these combinations are not valid since they have all members of men
The correct answer is 20-1 = 19. Ans D
Answer: (D) 19
Question: I have twenty 3g stamps and twenty 5g stamps. Using one or more of these stamps, how many
different amounts of postage can I make?
(A) 150
(B) 152
(C) 154
(D) 396
(E) 400
Rationale: We need to find how many positive integers can be represented in the form 3n+5m
where n and m are integers between 0 and 20, but not with both of them 0. First, let us see
which integers divisible by 3 can be represented in this form. These are 3; 6; 9; ; 60 if we
set m = 0, and if we let m be 3; 6; 9; 12; 15; or 18, we get that the multiples of 3 we can
represent are 3; 6; 9; ; 150. There are thus 50 multiples of 3 we can represent. Working
similarly, we get that 5; 8; 11; ; 155 are the integers which give remainder 2 when divided
by 3, and which we can represent, giving 51 numbers of this form. Finally, the numbers which
give remainder 1 when divided by 3, and which can be represented in the desired form, are
10; 13; 16; ; 160. There are 51 of them. So, the answer is 50 + 51 + 51 = 152.
correct answer B
Answer: (B) 152
Question: If a, b, c, and d are integers; w, x, y, and z are prime numbers; w < x < y < z; and (wa)(xb)(yc)(zd)=660(wa)(xb)(yc)(zd)=660, what is the value of (a + b) – (c + d)?
(A) –1
(B) 0
(C) (a + b) – (c + d)=1
(D) 2
(E) 3
Rationale: 660660= 2^2 x 3^1 x 5^1 x 11^1
w < x < y < z = 2 < 3 < 5 < 11
So, can can say -
w = 2
x = 3
y = 5
z = 11
Hence a = 2 , b = c = d = 1
(a + b) – (c + d) will be (2 + 1) – (1 + 1) = 1
Answer will be (C)
Answer: (C) (a + b) – (c + d)=1
Question: A goods train runs at the speed of 72 km/hr and crosses a 150 m long platform in 26 sec. What is the length of the goods train?
(A) 370
(B) 782
(C) 278
(D) 270
(E) 881
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 150)/26 = 20
x = 370 m.
Answer: A
Answer: (A) 370
Question: A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook?
(A) 10
(B) 8
(C) 6
(D) 4
(E) 2
Rationale: Let the price of each note book be Rs.x.
Let the number of note books which can be brought for Rs.300 each at a price of Rs.x be y.
Hence xy = 300
=> y = 300/x
(x + 5)(y - 10) = 300 => xy + 5y - 10x - 50 = xy
=>5(300/x) - 10x - 50 = 0 => -150 + x2 + 5x = 0
multiplying both sides by -1/10x
=> x2 + 15x - 10x - 150 = 0
=> x(x + 15) - 10(x + 15) = 0
=> x = 10 or -15
As x>0, x = 10.
ANSWER:A
Answer: (A) 10
Question: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 6-letter code words?
(A) 1
(B) 1/4
(C) 1/5
(D) 1/3
(E) 1/2
Rationale: Method #1: Using the permutation formula
# of 5 letter code words:
nPr = n! / (n – r)! = 10! / (10 – 5)! = 10*9*8*7*6
# of 6 letter code words:
nPr = 10! / (10 – 6)! = 10*9*8*7*6*5
# of 5 words / # of 4 words = (10*9*8*7*6)/(10*9*8*7*6*5) = 1/5
C
Answer: (C) 1/5
Question: What is 120% of 13/24 of 960?
(A) 420
(B) 484
(C) 526
(D) 578
(E) 624
Rationale: 120% * 13/24 * 360 = 1.2 * 13 * 40 = 624
The answer is E.
Answer: (E) 624
Question: A man can row 40km upstream and 55km downstream in 13 hours also, he can row 30km upstream and 44km downstream in 10 hours. find the speed of the man in still water and the speed of the current.
(A) 5 and 3
(B) 8 and 3
(C) 3 and 8
(D) 3 and 5
(E) None of them
Rationale: let rate upstream=x km/hr and rate downstream=y km/hr.
Then,40/x +55/y =13…(i) and 30/x +44/y =10
Multiplying (ii) by 4 and (i) by 3 and subtracting ,we get:11/y=1 or y=11.
Substituting y=11 in (i),we get:x=5.
Rate in still water =1/2(11+5)kmph=8kmph.
Rate of current=1/2(11-5)kmph=3kmph
Answer is B.
Answer: (B) 8 and 3
Question: A single reservoir supplies the petrol to the whole city, while the reservoir is fed by a single pipeline filling the reservoir with the stream of uniform volume. When the reservoir is full and if 40,000 liters of petrol is used daily, the suply fails in 90 days.If 32,000 liters of petrol is used daily, it fails in 60 days. How much petrol can be used daily with out the supply ever failing?
(A) 64000 liters
(B) 56000 liters of petrol
(C) 78000 liters
(D) 60000 liters
(E) None of these
Rationale: Explanation:
Let x liter be the per day filling and v litr be the capacity of the reservoir, then
90x + v = 40000 × 90 -----(1)
60x + v= 32000 × 60 ------(2)
solving eq.(1) and (2) , we get
x = 56000
Hence , 56000 liters per day can be used without the failure of supply.
Answer: B
Answer: (B) 56000 liters of petrol
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 180 m
(B) 200 m
(C) 240 m
(D) 320 m
(E) None
Rationale: Sol.
Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x metres.
Then, x + 300 / 36 = 15 ⇔ x + 300 = 540 ⇔ x = 240 m.
Answer C
Answer: (C) 240 m
Question: If p#q denotes the least common multiple of p and q, then T=((12#16)#(18#24)) = ?
(A)  216
(B)  180
(C)  144
(D)  108
(E)  72
Rationale: There are several ways to find the Least Common Multiple of two numbers. In this case, the most efficient method is to use the Greatest Common Factor: (A * B) / (GCF AB) = LCM AB
The greatest common factor of 12 and 16 is 4. So, 12#16 = 12*16/4 = 48.
The greatest common factor of 18 and 24 is 6. So, 18#24 = 18*24/6 = 72
Finally, the greatest common factor of 48 and 72 is 24. So,T= ((12#16)#(18#24)) = 48#72 = (48*72)/24 = 2*72 = 144
The correct answer is C.
Answer: (C)  144
Question: In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 4 rows in all and a total of 134 bricks in the wall, how many bricks does the bottom row contain ?
(A) 30
(B) 31
(C) 32
(D) 33
(E) 34
Rationale: The bottom row has x bricks
x+x-1+x-2+x-3 = 134
4x-6=134
4x=128
x=32
Answer:C
Answer: (C) 32
Question: A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
(A) Rs.14000
(B) Rs.1000
(C) Rs.10500
(D) Rs.2050
(E) Rs.5500
Rationale: Explanation:
25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = Rs.14000
ANSWER:A
Answer: (A) Rs.14000
Question: Machine A can finish a job in 6 hours, Machine В can finish the job in 12 hours, and Machine С can finish the job in 8 hours. How many hours will it take for A, B, and С together to finish the job?
(A) 6/5
(B) 7/4
(C) 8/3
(D) 9/2
(E) 12/5
Rationale: The combined rate is 1/6+1/12+1/8 = 9/24 of the job per hour.
The time to complete the job is 24/9 = 8/3 hours.
The answer is C.
Answer: (C) 8/3
Question: How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 2 ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 0
Rationale: A number ending with 2 can never be a perfect square.
Answer: E
Answer: (E) 0
Question: Diesel costs Rs.4 per lit and petrol costs 6.83 per litre. If the price of diesel rise by 10% a month and the price of petrol is unchanged.How many months will it take until a litre of Diesel costs more than a litre of petrol.
(A) 9 months
(B) 5 months
(C) 6 months
(D) 3 months
(E) 2 months
Rationale: Explanation :
=>In the First Month the price of the diesel would be 4*110/100 = 4.4
=>In the Second Month the price of the diesel would be 4.4*110/100 = 4.84
=>In the Third Month the price of the diesel would be 4.84*110/100 = 5.324
=>In the fourth Month the price of the diesel would be 5.324*110/100 = 5.85
=>In the fifth Month the price of the diesel would be 5.85*110/100 = 6.44
=>In the sixth Month the price of the diesel would be 6.44*110/100 = 7.08 which is higher than the price of petrol
Answer : C
Answer: (C) 6 months
Question: y = 248 - 343x
Which of the following values of x gives the greatest value of y in the equation above?
(A)  200
(B)  100
(C)  -7
(D)  0
(E)  10
Rationale: Clearly, the negative value of x will result in maximum value of y.
Don't even look at the rest of the answer choices as only one negative value is being present.
Answer is C
Answer: (C)  -7
Question: Reena took a loan of 1000 with simple interest for as many years as the rate of interest. If she paid 40 as interest at the end of the loan period, what was the rate of interest?
(A) 3.8
(B) 2
(C) 6
(D) Cannot be determined
(E) None
Rationale: Explanation: Let rate = R% and time = R years.
Then, (1000 x R x R)/100 = 40
10RÂ² = 40
RÂ² = 4
R = 2.
Answer: Option B
Answer: (B) 2
Question: Evaluate 28% of 450 + 45% of 280
(A) 232
(B) 242
(C) 252
(D) 262
(E) 250
Rationale: Explanation:
= (28/100) * 450 + (45/100) * 280
= 126 + 126 = 252
Answer IS C
Answer: (C) 252
Question: If a:b = 4:1, then find (a - 3b)/(2a - b)?
(A) 6/7
(B) 1/7
(C) 5/7
(D) 3/2
(E) 4/7
Rationale: Answer: Option B
a/b = 4/1 => a = 4b
(a - 3b)/(2a - b) = (4b - 3b)/(8b - b)
= b/7b => 1/7
Answer: (B) 1/7
Question: In a car wheel, two spokes cover 10 degree. Then for the entire car,how many spokes are there?
(A) 128
(B) 168
(C) 248
(D) 268
(E) 288
Rationale: given, 2 spokes cover 10degrees,
so for 360 degrees.---->360*2/10=72..
so, for entire car, 4*72=288
ANSWER:E
Answer: (E) 288
Question: If one-third of one-fourth of a number is 15, then three-tenth of that number is
(A) 35
(B) 15
(C) 60
(D) 54
(E) 57
Rationale: Let the number be x. then 1/3 of ¼ of x=15
X=15x12=180
The required number=(3/10)*180=54
ANSWER D 54
Answer: (D) 54
Question: If x and y are both integers such that 41y = 36x and y is not negative, which of the following must be true?
(i) x is prime
(ii) y is even
(iii) xy is positive
(A) ii only
(B) iii only
(C) i and iii only
(D) ii and iii only
(E) i, ii and iii
Rationale: Effectively y = 36x/41
(i) x is prime: now if y = 36x/41 and both x and y are integers; then if x= 41, 36(41)/41 .....so the 41s cancel each other out and you get x=36. Hunky dory. But if x = 82; you get y =72 which also works. Hence x is not necessarily prime.
(ii) y is even: y = 36(41)/41 = 36 (even). Or try 36(82)/41 = 72 (even). When you multiply even with odd, answer is even. So Y HAS TO BE EVEN.
(iii) xy is positive. Hmm. So if y is positive, then x is positive. Because if you have a -ve value of x, it leads to -ve value of y. Hence I would say iii is the answer. ANSWER:B
Answer: (B) iii only
Question: A certain company has budgeted $1560 for entertainment expenses for the year, divided into 12 equal monthly allocations. If by the end of the third month, the total amount spent on entertainment was $420, how much was the company under budget or over budget?
(A) $60 under budget
(B) $30 under budget
(C) $30 over budget
(D) $60 over budget
(E) $180 over budget
Rationale: The budget for 3 months is (3/12)*$1560 = $390
The company is $30 over budget.
The answer is C.
Answer: (C) $30 over budget
Question: In a consignment of eggs 552 were cracked, which was 12 percent of the total consignment. How many eggs were in the consignment?
(A) 4400
(B) 4800
(C) 4300
(D) 4600
(E) 4900
Rationale: D
4600
(552 ÷ 12) × 100 = 4600.
Answer: (D) 4600
Question: P,Q and R together earn Rs.1800 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?
(A) s.50
(B) s.70
(C) s.90
(D) s.100
(E) s.120
Rationale: Explanation :
Amount Earned by P,Q and R in 1 day = 1800/9 = 200 ---(1)
Amount Earned by P and R in 1 day = 600/5 = 120	---(2)
Amount Earned by Q and R in 1 day = 910/7 = 130	---(3)
(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day
- Amount Earned by P,Q and R in 1 day = 120+130-200 = 50
=>Amount Earned by R in 1 day = 50
Answer : Option A
Answer: (A) s.50
Question: A certain meter records voltage between 0 and 10 volts inclusive. If the average value of 3 recordings on the meter was 6 volts, what was the smallest possible recording in volts?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: if average of 3 is 6 so sum of 3 should be 18
3 recording can be from 0-10 inclusive
to find one smallest other two should be highest
so, lets assume three var are a,b,c
say a is smallest and give b and c greatest readings say 8 and 8
so a has to be 2
A
Answer: (A) 2
Question: A sum of money becomes triple itself in 5 years at simple interest. How many years will it become nine times at the same rate?
(A) 12 Â½ years
(B) 62 Â½ years
(C) 18 Â½ years
(D) 72 Â½ years
(E) 12 Â½ years
Rationale: 100 ---- 200 ---- 5
200 ---- 5
100 ---- 2 1/2
------------------
900 ---- 18 Â½ years
Answer:C
Answer: (C) 18 Â½ years
Question: A and B start from house at 10am. They travel on the MG road at 20kmph and 40 kmph. there is a Junction T on their path. A turns left at T junction at 12:00 noon, B reaches T earlier, and turns right. Both of them continue to travel till 2pm. What is the distance between A and B at 2 pm
(A) 160kilometre
(B) 170km
(C) 180km
(D) 190km
(E) 150km
Rationale: at 12 A will travel=20*2= 40km
B will travel this 40 km in 40/40=1 hr i.e. by 11am.
after T junction for A- distance travelled =2*20=40 km
for b distance travelled =40*3=120
so distance between A & B is=120+40=160km
ANSWER:A
Answer: (A) 160kilometre
Question: A car salesman earns a base salary of $800 per month plus a commission of $200 for each car he sells. If the car salesman earned $2600 in September, how many cars does he need to sell in October in order to double his September earnings?
(A) 18
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: 800+200x=5200
x=22 cars.
The answer is E.
Answer: (E) 22
Question: What is the place value of 2 in the numeral 12734?
(A) 1500
(B) 4500
(C) 2000
(D) 6000
(E) 4000
Rationale: Option 'C'
2 * 1000 = 2000
Answer: (C) 2000
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: 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 - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.
Answer: Option B
Answer: (B) 50
Question: In how many different number of ways a Committee of 3 person of can be selected from 5 boys and 3 girls such that at least 1 girl is included in the committee
(A) 41
(B) 42
(C) 46
(D) 48
(E) 50
Rationale: 1G 2B 2G 1B 3G
= 3C1 × 5C2 + 3C2 × 5C1 + 3C3s
= 3 × (5 × 4)/2 + 3 × 5 + 1
= 30 + 15 + 1 = 46
Total 5M 3W
8C3 = 56
5C3 = 10
At least one girl = total - with out girl
At least one girl = 56 - 10 = 46
C)
Answer: (C) 46
Question: A car gets 32 miles to the gallon. If it is modified to use a solar panel, it will use only 80 percent as much fuel as it does now. If the fuel tank holds 12 gallons, how many more miles will the car be able to travel, per full tank of fuel, after it has been modified?
(A) 84
(B) 88
(C) 92
(D) 96
(E) 100
Rationale: Originally, the distance the car could go on a full tank was 12*32=384 miles.
After it has been modified, the car can go 32/0.8= 40 miles per gallon.
On a full tank, the car can go 12*40= 480 miles, thus 96 miles more.
The answer is D.
Answer: (D) 96
Question: When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy works alone she chops 3 lb. salad in 2 minutes. They start working together, and after some time finish chopping 65 lb. of salad. Of those 80 lb., the salad quantity chopped by Tammy is what percent greater than the quantifying chopped by Tom?.
(A) 44%
(B) 125%
(C) 105%
(D) 225%
(E) 400%
Rationale: Tom chops 4 lbs in 6 minutes
Tammy chops 9 lbs in 6 minutes
So in the same amount of time, Tammy chops 125% more than Tom, since 9 is 125% greater than 4. So 125% is the answer.
Note that the actual time doesn't matter. If you multiply the time each work by x, you'll multiply the work each does by x, and 9x is still 125% greater than 4x.
Ans : B
Answer: (B) 125%
Question: Twelve animals of a circus has to be placed inside in twelve cages one in each cage. If 4 of the cage are too small for 6 of the animal then find the number of ways of caging the animal.
(A) A.604800
(B) B.808250
(C) C.502450
(D) D.784200
(E) E.4838400
Rationale: ways for cages that are too small = 5*4*3*2=120
since we have 8 cages and 8 animal left therefore ways for 8 cages =8!
total ways =120*8!=4838400
Answer E
Answer: (E) E.4838400
Question: There are 45 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?
(A) 4
(B) 7
(C) 17
(D) 21
(E) 27
Rationale: let's find the range of Both and hence the range of x. Minimum value of Both: Say there is no overlap in the two sets.45 = x + 2xx =15In this case Both = 0 Maximum value of Both: Say there is maximum overlap between the two sets. One set has x so it could be a subset of the set 2x.45 = 2xBut x cannot be a decimal so (x-1) could be the overlap (= Both) and there could be 1 in only the Golf club.45 = 2 x + x - (x - 1)x = 22In this case Both = 22 - 1 = 21 So Both lies between 0 and 21 Only option (C) satisfies this condition. ANSWER:C
Answer: (C) 17
Question: A certain number when divided by 110 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Explanation:
110 + 25 =135/15 = 9 (Remainder)
E
Answer: (E) 9
Question: Alpha, Beta and Gamma are inner angles in a triangle. If Alpha = Beta + Gamma, what can't be the size of Beta?
(A) 44 degrees
(B) 45 degrees.
(C) 89 degrees
(D) 90 degrees.
(E) There isn't enough data to determine.
Rationale: Given Alpha = Beta + Gamma, and Alpha, Beta and Gamma are inner angles in a triangle. Thus Alpha + Beta + Gamma = 180
Beta + Gamma + Beta + Gamma = 180 => 2(Beta + Gamma) = 180 => Beta + Gamma = 90. Thus beta will be less than 90.
Hence the answer is D.
Answer: (D) 90 degrees.
Question: The sum of the squares of three consecutive odd numbers is 2531.Find the
numbers.
(A) 27,28 and 31
(B) 25,29 and 31
(C) 27,29 and 32
(D) 26,33 and 31
(E) 27,29 and 31
Rationale: Let the numbers be x, x + 2 and x + 4.
Then, X2 + (x + 2)2 + (x + 4)2 = 2531 => 3x2 + 12x - 2511 = 0
=> X2 + 4x - 837 = 0	=> (x - 27) (x + 31) = 0	=>	x = 27.
Hence, the required numbers are 27, 29 and 31.
Answer is E.
Answer: (E) 27,29 and 31
Question: Mrs. Napier has 45 stickers to give to 7 students for a reward. How many
stickers will each student get? Will there be any stickers left over?
(A) 2-5
(B) 6-4
(C) 2-6
(D) 2-3
(E) 2-8
Rationale: 45/7 = 6 R 4 Mrs. Napier will give each student 6 stickers and there
will be 4 left over.
correct answer B
Answer: (B) 6-4
Question: What is the probability that an integer selected randomly from 101 to 550, inclusive, begins with 1, 2, or 3, and ends with 4, 5, or 6?
(A) 1/5
(B) 2/5
(C) 3/5
(D) 1/4
(E) 1/3
Rationale: Total = 550-101+1= 450
Desired values= 3*10*3 = 90
P(A) = 90/450 = 1/5
ANSWER:A
Answer: (A) 1/5
Question: A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:
(A) Rs. 14,000
(B) Rs. 14,200
(C) Rs. 14,400
(D) Rs. 14,700
(E) Rs. 14,800
Rationale: Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
A's share = Rs. (35000 x 21/50) = Rs. 14,700.
D
Answer: (D) Rs. 14,700
Question: Robert left from a Pvt Company. Management hold his salary Rs. 15000/- for one month. Earlier Robert borrowed Rs. 7280/- from company. But Robert forget that. After one month Robert asked his salary and accountant gives Rs.18500/- to him. What is the incentive amount given to Robert?
(A) 9500
(B) 12500
(C) 10780
(D) 10500
(E) 8600
Rationale: Total Salary = Rs.15000/-
Borrowed Money = 7280/-
Balance Salary = 15000-7280= 7720
Paid amount = 18500/-
Incentive amount = 18500-7720 = 10780/-
Answer is C
Answer: (C) 10780