divelab/Sys2Bench huggingface dataset:
Question: The number x yields a remainder p when divided by 13 and a remainder q when divided by 7. If p = q + 7, then which one of the following could be the value of x ?
Options:
A)45
B)36
C)72
D)85
E)100
Rationale: I solved this question in the following way:
Q<7 so Q can be from 0 to 4 and P<13 so P can be from 0 to 12, BUT the constraint is P=Q +7 so this will mean that P can be in the range from 7 to 12.
x=13k + P or x= 13k + 7 to 12 and look at the answer as, place different values for k, B will give 36 which is 13*2 + 10, the other answers are out of the range
Answer: B
Question: The daytime telephone rate between two cities is 60 cents for the first 3 minutes and c cents for each additional minute. The total charge is reduced 60 percent on calls made after 10:00 P.M. The cost, in dollars, of a 33-minute call made at 10:30 P.M. between these two cities is:
Options:
A) 0.4(0.60) + 35c
B) 0.4(0.60 + 9c)
C) 0.4(0.60 + 0.30c)
D) 0.6(0.60 + 30c)
E) 0.6(0.60 + 0.35c)
Rationale: For first three minutes = 60 cents
Remaining minutes = 33 -3 = 30
charge for 32 minutes = 30c
total cost (if the call was made in daytime) = 0.60 + 30c
60% chargereducedon night calls => 40% charge
=>0.4(0.60 + 30c)
Hence, Answer is C
Answer: C
Question: suga invested an amount of Rs. 10,500 at the rate of 13% p.a simple interest and another amount at the rate of 15% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested?
Options:
A)13650
B)13150
C)13450
D)13900
E)13750
Rationale: Let the second amount be Rs. x. Then,
(10500 * 13 * 1)/100 + (x * 15 * 1)/100 = [(12000 + x) * 14 * 1] / 100
13650+ 15x= 16800 + 14x
x = 3150
Total investment = 10000 + 3150 = Rs. 13150 .Answer: B
Answer: B
Question: A train 480 m long passed a pole in 12 sec. How long will it take to pass a platform 560 m long?
Options:
A)76 sec
B)29 sec
C)26 sec
D)15 sec
E)16 sec
Rationale: Speed = 480/12 = 40 m/sec.
Required time = (480 + 560)/40
= 26 sec.
Answer:C
Answer: C
Question: In how many different ways can 3 boys and 2 girls sit on a bench such that the girls always sit together?
Options:
A)44
B)48
C)52
D)56
E)60
Rationale: We can think of the girls as one unit.
The number of ways to arrange 4 units in order is 4!
The girls can have different arrangements, so we multiply this by 2!
The number of ways to sit is 4!*2!=48
The answer is B.
Answer: B
Question: A merchant sells his two cars – one at 15% loss and another at 12% profit. If the cost prices of the two cars are in the ratio of 1:2, what is his percent profit or loss?
Options:
A)3% profit
B)2% loss
C)2% profit
D)3% loss
E)None of these
Rationale: Explanation:
Given that CPs are in the ratio 1:2
Therefore let the CPs be Rs.100 & Rs.200 respectively,
1st SP = 100-15% of 100 = Rs.86.
2nd SP = 200 + 12% of 200 = Rs.224.
Total CP = Rs.300. Total SP = 85+224 = Rs.309.
Profit = Rs.309-300 = Rs.9.
Profit percent = 9x100/300 = 3% profit.
Answer: Option A
Answer: A
Question: Find the odd man out. 5, 10, 40, 81, 320, 640, 2560
Options:
A)40
B)81
C)320
D)2560
E)640
Rationale: Explanation :
Alternatively 2 and 4 are multiplied with the previous terms
5
5 × 2 = 10
10 × 4 = 40
40 × 2 = 80
80 × 4 = 320
320 × 2 = 640
640 × 4 = 2560
Hence, 81 is wrong. 80 should have come in place of 81.
Answer : Option B
Answer: B
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)767 m
B)674 m
C)245 m
D)187 m
E)765 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2
=> 2(130 + x) = 750 => x = 245 m.
Answer: C
Answer: C
Question: The S.I. on a certain sum of money for 3 years at 5% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
Options:
A)2197
B)2800
C)1750
D)2267
E)1262
Rationale: Explanation:
C.I. = [4000 * (1 + 10/100)2 - 4000]
= (4000 * 11/10 * 11/10 - 4000) = Rs. 840.
Sum = (420 * 100)/(3 * 5) = Rs. 2800
Answer:B
Answer: B
Question: A batsman makes a score of 300 runs in the 17th inning and thus increases his averages by 10. What is his average after 17th inning?
Options:
A)39
B)140
C)42
D)40.5
E)41.5
Rationale: let the average after 16th inning =x
then total run after 16th inning=16x
then total run after 17th inning=16x+300
then average run after 17th inning=(16x+300)/17
(16x+300)/17=x+10 => 16x+300 = 17x+170
x=130
average after 17th inning =130+10=140
ANSWER:B
Answer: B
Question: If x ≠ 0 and x^2 - (2- x^2)/x^2 = y/x, then y =
Options:
A)-2/x
B)x^2 − 2
C)2x^2 − 2
D)x − 2 − x^2
E)x − 2 + x^2
Rationale: x^2 - (2- x^2)/x^2 = y/x
-2/x^2 = y/x
y = -2/x
Answer : A
Answer: A
Question: Which of the following is a possible length for side AB of triangle ABC if AC = 3 and BC = 10?
I. 7
II. 9 √3
III. 11.5
Options:
A)I only
B)II only
C)III only
D)II and III
E)I, II, and III
Rationale: (10-3) < AB < (10+3)
The answer is C.
Answer: C
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:
Options:
A)2700
B)2900
C)3000
D)3100
E)3300
Rationale: Number of valid votes = 80% of 7500 = 6000.
Valid votes polled by other candidate = 45% of 6000
=45/100 x 6000 = 2700
ANSWER :A
Answer: A
Question: Five years ago, the average age of A and B was 15 years. Average age of A, B and C today is 20 years. How old will C be after 20 years?
Options:
A)30
B)35
C)40
D)50
E)60
Rationale: Explanation :
(A + B), five years ago = (15 * 2) = 30 years.
(A+B), now = (30+5*2)years=40 years.
(A + B + C), now = (20 x 3) years =60 years.
C, now = (60 - 40) years = 20 years.
C, after 20 years = (20 + 20) years =40 years.
Answer : C
Answer: C
Question: A cistern is filled by pipe A in 16 hours and the full cistern can be leaked out by an exhaust pipe B in 20 hours. If both the pipes are opened, in what time the cistern is full?
Options:
A)50hrs
B)60hrs
C)70hrs
D)80hrs
E)90hrs
Rationale: time taken to full the cistern=(1/16-1/20)hrs
=1/80
=80hrs
ANSWER:D
Answer: D
Question: 21 goats eat as much as 15 cows. How many goats each as much as 35 cows?
Options:
A)49
B)32
C)36
D)41
E)42
Rationale: Explanation :
15 cows ≡ 21 goats
1 cow ≡21/15 goats
35 cows ≡ (21×35)/15 goats ≡ (21×7/3) goats ≡ 7 × 7 goats ≡ 49 goats. Answer : Option A
Answer: A
Question: The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ?
Options:
A)150
B)185
C)190
D)210
E)220
Rationale: 185
Answer is B
Answer: B
Question: Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points?
Options:
A)87
B)83
C)78
D)56
E)32
Rationale: We know that, the number of straight lines that can be formed by the 11 points in which 6 points are collinear and no other set of three points, except those that can be selected out of these 6 points are collinear.
Hence, the required number of straight lines
= ¹¹C₂ - ⁶C₂ - ⁵C₂ + 1 + 1
= 55 - 15 - 10 + 2 = 32
Answer:E
Answer: E
Question: A trader bought a car at 30% discount on its original price. He sold it at a 70% increase on the price he bought it. What percent of profit did he make on the original price?
Options:
A)18%
B)13%
C)12%
D)32%
E)19%
Rationale: Original price = 100
CP = 70
S = 70*(170/100) = 119
100 - 119= 19%
Answer: E
Answer: E
Question: A right triangle has its other two angle measurements given in ratios 2:3 relative to each other. What is the measurement of one of the other two angles?
Options:
A)36Â°
B)45Â°
C)60Â°
D)74Â°
E)86Â°
Rationale: A right triangle has a 90Â° angle, so the other two angles should add up to 90Â°. With the 2:3 ratio, we use the equation
2x + 3x = 90Â°
5x = 90Â°
x = 18Â°
2x = 36Â°, which is A
3x = 54Â°, which is not in the choices, so the answer is A
Answer: A
Question: A table is bought for Rs.400/- and sold at Rs.300/- find gain or loss percentage
Options:
A)25%loss
B)30%gain
C)25%gain
D)10%loss
E)50% loss
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (300 - 400)/400 = 25% loss
A
Answer: A
Question: What is 2 2/3 - 1 1/4 divided by 1/5 - 1/6 ?
Options:
A)17/36
B)36/17
C)17/6
D)85/2
E)51/4
Rationale: 2 2/3 - 1 1/4 = 8/3 - 5/4 = (32 - 15 )/12 = 17/12
1/5 - 1/6 = (6-5)/30 = 1/30
So 17/12/1/30 = 17/12 * 30 = 85/2
Answer - D
Answer: D
Question: IF
1= E
2=O
3= E
4= R
5= I
THEN 6=?
Options:
A)I
B)J
C)K
D)X
E)M
Rationale: IF
1= E... last letter of ONE.
2=O.... last letter of TWO.
3= E
4= R
5= E
THEN 6=X ... last letter of SIX.
ANSWER:D
Answer: D
Question: A committee is reviewing a total of 20x black-and-white films and 4y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction of the selected films are in color?
Options:
A)26/21
B)28/21
C)20/21
D)40/21
E)60/21
Rationale: Say x=y=10. In this case we would have:
20x=200 black-and-white films;
4y=40 color films.
y/x%=10/10%=1% of the black-and-white films, so 2 black-and-white films and all 40 color films, thus total of 42 films were selected.
Color films thus compose 40/42=20/21 of the selected films.
Answer: C
Answer: C
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 57, the how old is B?
A.	7
B.	8
C.	9
D.	10
Explanation:
Options:
A)5
B)22
C)9
D)10
E)11
Rationale: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 57
5x = 55
x = 11.
Hence, B's age = 2x = 22 years.
Answer: Option B
Answer: B
Question: Calculate the percentage gain if a trader bought a bicycle for Rs.740 and sold it for Rs.1250?
Options:
A)61.92%
B)68.92%
C)66.92%
D)63.92%
E)62.92%
Rationale: C.P. = 740
S.P. = 1250
Gain = 1250-740 ---- 510
% Gain => 510/740*100 => 68.92%
Answer:B
Answer: B
Question: The average of 7 consecutive numbers is 33. The highest of these numbers is:
Options:
A)28
B)30
C)33
D)36
E)28
Rationale: The average of 7 consecutive numbers will be the 4th number which is given to be = 33 5th number = 34, 6th number = 35, 7th number = 36
Answer: D.
Answer: D
Question: Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 – S1+S0. What is the value of K?
Options:
A)67
B)130
C)45
D)41
E)36
Rationale: I used brute force for this question:
S6: 36+30+94=160
S5: 25+25+94=144
S4: 16+20+94=130
S3: 9+15+94=118
S2: 4+10+94=108
S1: 1+5+94=100
S0: 0+0+94=94
S6-S5+S4-S3+S2-S1+S0= 16+12+8+94=130
Answer B
Answer: B
Question: Ayesha's father was 48 years of age when she was born while her mother was 40 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Options:
A)2 years
B)4 years
C)6 years
D)7 years
E)6 years
Rationale: Explanation:
Mother's age when Ayesha's brother was born = 40 years.
Father's age when Ayesha's brother was born = (48 + 4) = 52 years.
Required difference = (52 - 48) = 4 years.
Answer: Option B
Answer: B
Question: An urn contains 10 balls, numbered from 1 to 10. If 2 balls are selected at random with replacement from the urn, what is the probability N that the sum of the 2 numbers on the balls will be even?
Options:
A)25%
B)37.5%
C)50%
D)62.5%
E)75%
Rationale: Correct Answer: C
Since there are 5 even numbered balls and 5 odd numbered balls, the probability N of selecting either an even or an odd is 5/10= 1/2. In order for the sum of the numbers on the two balls to be even, either both numbers must be even or both numbers must be odd; one even and one odd number would add to an odd number. The probability of selecting two even numbers is:
1/2 * 1/2= 1/4
The probability of selecting two odd numbers is also:
1/2 * 1/2= 1/4
Adding both probabilities gives 1/4+1/4= 1/2 , or 50%, as the probability that the sum of the numbers will be even. Thus, the correct answer is (C).
Answer: C
Question: Two pipes can fill a tank in 20 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
Options:
A)5 minutes
B)17 minutes
C)15 minutes
D)10 minutes
E)12 minutes
Rationale: Part of the filled by all the three pipes in one minute
= 1/20 + 1/15 - 1/45 = (9 + 12 - 4)/180 = 17/180
So, the tank becomes full in 5 minutes.
Answer: A
Answer: A
Question: If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 9% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?
Options:
A)2
B)5
C)900/109
D)110/209
E)9/4
Rationale: Let price be 10/ticket
then 220 tickets for this month's performance at its usual price=2200
which is 10%greater than last month(let X)---->x(1+10/100)=2200----->x=2000
now new revenue this month=200*10.9=2180
as per question asked 2000=2180(1-A/100)----->A=900/109%
Ans C
Answer: C
Question: A number is selected at random from the first 30 natural numbers. What is the probability that the number is a multiple of either 2 or 19?
Options:
A)17/30
B)2/5
C)7/15
D)8/15
E)11/30
Rationale: Number of Multiples of 2 from 1 through 30 = 30/2 = 15
Number of Multiples of 19 from 1 through 30 = 30/19 = 1
Number of Multiples of 2 and 19 both from 1 through 30 = Number of Multiples of 19*2(=38) = 0
Total favourable cases = 15 + 1- 0 = 16
Probability = 16 / 30 = 8/15
Answer: option D
Answer: D
Question: A train is 360 meter long is running at a speed of 36 km/hour. In what time will it pass a bridge of 140 meter length?
Options:
A)50 seconds
B)29 seconds
C)40 seconds
D)11 seconds
E)12 seconds
Rationale: Speed = 36 Km/hr = 36*(5/18) m/sec = 10 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (1/10) = 50 seconds
Answer:A
Answer: A
Question: 15 people went to a hotel for combine dinner party 10 of them spent Rs. 50 each on their dinner and rest spent 4 more than the average expenditure of all the 15. What was the total money spent by them.
Options:
A)1628.4
B)1534
C)780
D)1496
E)None of these
Rationale: Solution: Let average expenditure of 15 people be x.
then,
15x = 10*50+5*(x+4);
Or, 15x = 10*50+5x+20;
Or, x = 52;
So, total money spent = 52*15 = Rs. 780.
Answer: Option C
Answer: C
Question: A train is 360 meter long is running at a speed of 90 km/hour. In what time will it pass a bridge of 140 meter length?
Options:
A)27 seconds
B)29 seconds
C)40 seconds
D)11 seconds
E)20 seconds
Rationale: Speed = 90 Km/hr = 90*(5/18) m/sec = 25 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (1/25) = 20 seconds
Answer:E
Answer: E
Question: A man bets on no. 16 on a roulette wheel 14 times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and is therefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what are the odds of winning on the bet that he takes?
Options:
A)23:41
B)Either ;35:1
C)41:54
D)35:43
E)12:31
Rationale: Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans.
Either ;35:1
B)
Answer: B
Question: How many positive integers less than 250 are multiple of 4 but NOT multiples of 6?
Options:
A)20
B)31
C)42
D)53
E)64
Rationale: Multiples of 4 less than 250 = {4,8,12,......248} = 62 numbers
Multiples of 4 which are multiples of 3 too ={12,24,36.....240} = 20 numbers
So required number= 62-20 = 42
Choice C
Answer: C
Question: When integer K is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?
I. 3K
II. 4K+10
III. 5K
IV. 2K
V .6K
II. 5n
III. 4n + 10
Options:
A)II
B)I
C)III
D)V
E)IV
Rationale: C
Answer: C
Question: How many positive integers less than 17 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?
Options:
A)14
B)13
C)12
D)11
E)10
Rationale: The number = 2a + 3b < 17
When a = 1, b = 1, 2, 3, 4, 5 -> 2a = 2; 3b = 3, 6, 9, 12, 15 -> the number = 5, 8, 11, 14-->4 numbers
when a =2, b = 1,2,3,4-> ....--> 4 numbers
when a =3, b = 1,2,3 --> ....--> 3 numbers
Total number is already 11. Look at the answer there is no number greater than 11 --> we dont need to try any more
Answer must be D
Answer: D
Question: The sum of ages of 5 children born 3 years different each is 55 yrs. What is the age of the Elder child?
Options:
A)17
B)19
C)16
D)18
E)21
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 55
5x = 25
x = 5.
x+12= 5+12= 17
A
Answer: A
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Options:
A)Rs.1000
B)Rs.1100
C)Rs.1200
D)Rs.1250
E)Rs.1500
Rationale: Explanation:
90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
A)
Answer: A
Question: Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is
Options:
A)35km/hr
B)30km/hr
C)32km/hr
D)34km/hr
E)36km/hr
Rationale: Distance covered = 120+120 = 240 m
Time = 12 s
Let the speed of each train = v. Then relative speed = v+v = 2v
2v = distance/time = 240/12 = 20 m/s
Speed of each train = v = 20/2 = 10 m/s
= 10×36/10 km/hr = 36 km/hr
Answer is E.
Answer: E
Question: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 1/4 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?
Options:
A)1/3
B)2/5
C)1/4
D)1/6
E)3/4
Rationale: The fraction of homes which are termite-infested but not collapsing is 3/4*1/3 = 1/4
The answer is C.
Answer: C
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?
Options:
A)20
B)43
C)45
D)80
E)90
Rationale: Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways
A
Answer: A
Question: P, Q and R are inner angles in a triangle. If P= Q+ R, what can't be the size of Q?
Options:
A)30 DEGREES
B)40 DEGREES
C)90 DEGREES
D)50 DEGREES
E)60 DEGREES
Rationale: Given P= Q+ R, and P, Q and R are inner angles in a triangle. Thus P+ Q+ R= 180
Q+ R+ Q+ R= 180 => 2(Q+ R) = 180 => Q+ R= 90. Thus Q will be less than 90.
Hence the answer is C.
Answer: C
Question: 4 red,6blue,26 green ball. person choose 1 at a time either blue or red. what is probability that he choose red ball
Options:
A)0.1
B)0.2
C)0.3
D)0.4
E)0.5
Rationale: probability that none of ball is blue or red is=26/36=13/18
probability of blue or red ball=1/13/18=5/18
probability of only red ball in blue or red ball=(4/36)/(5/18)=0.4
ANSWER:D
Answer: D
Question: Among 250 viewers interviewed who watch at least one of the three TV channels namely A, BC. 116 watch A, 127 watch C, while 107 watch B. If 90 watch exactly two channels. How many watch exactly one channel?
Options:
A)155
B)160
C)175
D)190
E)195
Rationale: 250 = n(Exactly 1 channel) + n(Exactly 2 channels) + n(Exactly 3 channels)
250 = n(Exactly 1 channel) + 90 + n(Exactly 3 channels)
Let's find the value of n(Exactly 3 channels) = x
250 = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)
Note that each of n(A and B) is the sum of 'number of people watching exactly two channels A and B' and 'number of people watching all three channels'.
250 = 116 + 127 + 107 - n(Exactly 2 channels) - 3x + x
250 = 116 + 127 + 107 - 90 - 2x
x = 25
250 = n(Exactly 1 channel) + 90 + 25
n(Exactly 1 channel) = 155
Answer (A)
Answer: A
Question: A start walking from a place at a uniform speed of 4 kmph in a particular direction. After half an hour, B starts from the same place and walks in the same direction as A at a uniform speed and overtakes A after 1 hour 48 minutes. Find the speed of B.
Options:
A)4.7 kmph
B)4.6 kmph
C)4 kmph
D)7 kmph
E)5.3 kmph
Rationale: Distance covered by A in 30 min = 1 Km
B covers extra 1km in 1 hour 48 minutes (9/5 hr)
i.e. Relative speed of B over A = 1/(9/5) = 5/9
So the speed of B = Speed of A + 5/9
= 4 + 5/9
= 4.55
Answer B
Answer: B
Question: A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.15 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?
Options:
A)1276
B)1200
C)2832
D)1800
E)1236
Rationale: Explanation:
l * 30 = 1200 è l = 40
40 + 30 + 50 = 120
120 * 15 = 1800
Answer: Option D
Answer: D
Question: Of the five numbers in a sequence, the first term is 10,000, and each of the following terms is 50% of the previous term. What is the value range of the five numbers?
Options:
A)9,375
B)9,750
C)9,975
D)9,984
E)10,736
Rationale: 1st number= 10,000
2nd number =50% of 10,000=5000
3rd number= 50% of 5000= 2500
4th number = 50% of 2500=1250
5th number= 50% of 1250= 625
Range = 10,000-625= 9375
A is the answer
Answer: A
Question: Tom bought 2 shares and sold them for $110 each. If he had a profit of 10% on the sale of one of the shares but a loss of 50% on the sale of the other share, then on the sale of both shares Tom had
Options:
A) a profit of $100
B) a loss of $100
C) a loss of $110
D) a profit of $110
E) neither a profit nor a loss
Rationale: total CP = 11000/110 + 11000/50 = 100 + 220=320
SP=110*2=220
loss= Rs 100/-
Answer: B
Answer: B
Question: Josh spends a total of $5.5 buying P items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then may be which of the following?
Options:
A)99
B)100
C)101
D)112
E)113
Rationale: P items in the convenience store$5.5 = 550 cents
550 = 50a + 5b
=>110 = 10a + b
b = 110 - 10a = 10(11-a)
Hence b is even and multiple of 10.
Possible values of b:
b = 10,20,30,40,50,60,70,80,90,100
a = 11,9,8,7,6,5,4,3,2,1
The total (a+b) is 21,29,38,47,56,65,74,83,92,101
The only option is 101. Hence C.
Answer: C
Question: There are 300 seniors at Morse High School, and 50% of them have cars. Of the remaining grades (freshmen, sophomores, and juniors), only 10% of them have cars. If 18% of all the students at Morse have cars, how many students are in the three lower grades?
Options:
A)600
B)900
C)1200
D)1350
E)1500
Rationale: Let x be the number of students in the lower three grades.
0.1x + 150 = 0.18(x+300)
0.08x = 96
x = 1200
The answer is C.
Answer: C
Question: The average age of 25 students in a group is 12 years. when teacher's age is included to it, the average increases by one.What is the teacher's age in years?
Options:
A)31
B)38
C)39
D)40
E)57
Rationale: age of the teacher=(26*13-25*12)
=38 years.
ANSWER:B
Answer: B
Question: A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 30% while buying and by 10% while selling. What is his percentage profit?
Options:
A)10.22%
B)20.22%
C)21.22%
D)30%
E)Can't be calculated
Rationale: The owner buys 100kg but actually gets 130kg;
The owner sells 100kg but actually gives 90kg;
Profit: (130-90)/90*100=30%
Answer: D.
Answer: D
Question: Tina has 5 socks and 3 pair of shoes. How many combinations does Barbara have, if she doesn’t wear 2 specific socks with 1 specific pair of shoes?
Options:
A)4
B)7
C)10
D)11
E)13
Rationale: Total no of combinations available is= 5 Socks X 3 pair of shoes = 15
Eliminate the 2 socks X 1 pair of shoes combo = 2 which gives.......>> 15-2=13
ANSWER: E
Answer: E
Question: Find the common ratio of three numbers in G.P whose product is 216 and the sum of the products taken in pairs is 114.
Options:
A)2 or ½
B)2/3 or 3/2
C)¾ or 4/3
D)4 or ¼
E)5 or 1/5
Rationale: Let the terms be a/r, a , ar
a/r *a * ar = a 3 =216, a =6
(a/r*a )+ (a*ar) + (ar*a/r ) =114, a 2/r + a 2 r + a 2 =114
a 2 ( 1/r + r +1 ) = 114, 36[( 1+ r 2 +r )/r] =114
6 [( 1 +r 2+ r )/r ]= 19, 6 r 2 -13 r + 6 = 0,
On solving, r = 2/3 or 3/2
ANSWER:B
Answer: B