divelab/Sys2Bench huggingface dataset:
Question: An exam consists of 2 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 70% is a passing grade, what is the probability that Brian passes?
Options:
A)1/16
B)37/256
C)1/2
D)219/256
E)15/16
Rationale: If you have 8 T or F and Brian is going to guess then each question he has a 50% chance of getting correct.
If a passing score is 70% it means Brian needs to get 6/8=75%, 7/8=87.5%, or 8/8=100% to pass. Each is a possibility. If Brian gets a 5/8(=62.5%) or below he fails.
So first figure out the number of ways that Brian can get 6 out of 8, 7 out of 8, and 8 out of 8 questions correct.
Which is 8 choose 6, equals is 28, 8 choose 7, equals 8, and 8 choose 8, equals 1. This sums to 37.
The number of possible questions outcomes -the sum of 8 choose 8, 7 choose 8, 6 choose 8….2 choose 8, 1 choose 8, and 0 choose 8 is 256, so the chance of him passing is 1/16.
A
Answer: A
Question: A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. Each block measures 1 by 1 meter. In how many different colors c patterns can be floor be parqueted?
Options:
A) 104
B) 213
C) 3^5
D) 705
E) 726
Rationale: Total number of squares we need to fill = 6
Number of colors we have = 3
Therefore, total number of patterns c= 3*3*3*3*3*3 = 729
However, this is considering that we can have a case in which all tiles are the same color. Since we are given that the quantity of each tile is 5 and the number of tiles required is 6, we know that this case cannot be possible. Therefore we must subtract the cases in which all tiles will be of the same color (3 cases since there are 3 colors).
Thus our answer should be :729 - 3 = 726
Answer : E
Answer: E
Question: How many integers between 1 and 1,050 are divisible by 10, 25, and 35?
Options:
A)4
B)5
C)6
D)7
E)3
Rationale: Prime factorization of given numbers
10=2*5
25=5^2
35=5*7
LCM of the given numbers
=2*5^2*7
=50*7
=350
Therefore , number of integers = 1050/350
=3
Answer:option E
Answer: E
Question: Akhil borrowed a certain sum of money at the rate of 6%, 9% and 14% for a period of first two years, next three years and beyond the period of five years respectively. If at the end of nine years, he paid Rs. 8550 as interest, then find the sum of money he had borrowed.
Options:
A)Rs. 9,002
B)Rs. 9,019
C)Rs. 9,199
D)Rs. 9,000
E)Rs. 9,192
Rationale: Explanation:
Let Rs.P be the money borrowed by Akhil.
I) R = 6%, T = 2 years
Simple Interest of 2 years = PRT/100
= P * 6 * 2/100 = 12P/100
II) R = 9%, T = 3 years
Simple Interest of 3 years = P * 9 * 3/100 = 27P/100
III) R = 14%, T = 4 years
Simple Interest of 3 years= P * 14 * 4/100 = 56P/100
Therefore, total Simple Interest of 9 years
= 12P/100 + 27P/100 + 56P/100
= 95P/100
The total interest paid after nine years = Rs.8550
95P/100 = 8550
Therefore, 95P = 855,000
P = 855,000/95 = Rs. 9,000
Amount of money borrowed by Akhil = Rs. 9,000
ANSWER: D
Answer: D
Question: Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $126 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?
Options:
A)600
B)720
C)1080
D)1200
E)1440
Rationale: We need to find the amount off Julie's Initial savings...Let that be 2x
So x goes in simple interest and x goes in compund interest for a period of 2 years...
In case of Simple interest, The interest paid out is same for each year..Hence if $120 was interest for 2 years that means interest per year will be 60 $
So we have S.I,120 = x∗2∗R100x∗2∗R100
or 6000 =x*R
For CI, in 126 $, 6$ represents nothing but interest earned on interest of 1st year.
In the First year, Interest amount is same for S.I and C.I
So we have
x(1+R100)2−x=126x(1+R100)2−x=126
or x(1 + R^2/10000+ 2R/100)-x=126
x+xR^2/10000+2xR/100)-x=126
x+R*6000/10000+12000/100-x=126
0.6R+120=126
0.6R=6 or R=10
So x=600...2x=1200 is the Initial savings. Answer is D
Answer: D
Question: A company that ships boxes to a total of 14 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (assume that the order of the colors in a pair does not matter)
Options:
A)7
B)8
C)5
D)9
E)6
Rationale: Back-solving is the best way to solve this problem.
You basically need 14 combinations (including single colors)
If we start from option 1->
1=> 4C2 + 4 = 10 (Not enough)
2=> 5C2 + 5 = 15 (Enough)
Since the minimum number is asked. It should be 5.
Answer - C
Answer: C
Question: The population of a town is 286900. If it increase at the rate of 5% per annum. What will be its population for 3years hence?
Options:
A)200000
B)215600
C)194582
D)332122
E)215460
Rationale: population after 3years = 286900*(1+ 5/100)^3 = 332122
Answer is D
Answer: D
Question: The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.1400, then what is the income of P1?
Options:
A)s.800
B)s.2400
C)s.4000
D)s.3500
E)s.4200
Rationale: Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their
expenditures be Rs.3y and 2y respectively.
Then, 5x – 3y = 1400 …(i) and 4x – 2y = 1400 ……..(ii)
On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 1400 -> x = 700
P1’s income = Rs 5*700 = Rs.3500
ANSWER:D
Answer: D
Question: Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 7020 km and comes back to the starting point. The total time taken by him is:
Options:
A)914.2 hours
B)900 hours
C)915 hours
D)891.4 hours
E)915 hours
Rationale: Explanation:
Speed downstream = (16 + 2) = 18 kmph
Speed upstream = (16 - 2) = 14 kmph
Total time taken = 7020/18 + 7020/14 = 390 + 501.4 = 891.4 hours
Answer: Option D
Answer: D
Question: Miles breeds Beagles and sells the puppies. He has nine customers that each want the same amount of puppies. Miles currently has 138 puppies. How many puppies would he have to keep to accommodate their requests?
Options:
A)1
B)4
C)5
D)8
E)3
Rationale: We add the sum of the digits together to get twelve and subtract to get a number that can be divided by 9. 12 - 9 = 3. This means Miles will have to keep three puppies(option D).
Answer: D
Question: Convert 100miles into yards?
Options:
A)25630 yards
B)35200 yards
C)39520 yards
D)42560 yards
E)176000 yards
Rationale: 1 mile = 1760 yards
100 miles = 100*1760 = 176000 yards
Answer is E
Answer: E
Question: How much time does a train 150 metres long running at 54 km/hr take to pass a pole?
Options:
A)7.9s
B)2.5s
C)7.5s
D)7.6s
E)10s
Rationale: Explanation:
54 km/hr = 54 * 5/18 = 15 m/s
Speed = distance/time; v = d/t
15 = 150/t
t = 10s
ANSWER: E
Answer: E
Question: Mike and Fritz ran a 30-mile Marathon. Mike ran 10 miles at 10 miles per hour and then ran at 5 miles per hour for the remaining 20 miles.Fritz ran the first one-third (by time) of the run at 10 miles per hour and the remaining two-thirds of the run at 5 miles per hour. How much time in hours did Fritz take to complete the Marathon?
Options:
A)3
B)3.5
C)4
D)4.5
E)5
Rationale: Let total time= t
F travelled at rate 10 mph for t/3 time and 5 mph for 2t/3 time
d= s1t1+s2t2
30= 10*t/3 + 5*2t/3
30= 20t/3
t= 4.5
D is the answer
Answer: D
Question: There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability Q that the number of men is equal to that of women?
Options:
A)Q=18/35
B)Q=16/35
C)14/35
D)13/35
E)12/35
Rationale: METHOD-1:
Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36
Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70
Probability = 36/70 = 18/35
A
METHOD-2:Also see the mistake done by the person who posted this question
Probability of First selected person being Man = 4/8
Probability of Second selected person being Man = 3/7
Probability of First selected person being Woman = 4/6
Probability of Second selected person being Woman = 3/5
i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35
The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here
When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well
The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!
A
Answer: A
Question: The average of 20 numbers is calculated as 30. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
Options:
A)40
B)26
C)60
D)97
E)12
Rationale: 20 * 30 + 36 – 26
= 160/10
= 60
Answer: 60
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)3398
B)2700
C)2887
D)2766
E)2981
Rationale: Total number of votes = 7500
Given that 20% of Percentage votes were invalid
=> Valid votes = 80%
Total valid votes =
1st candidate got 55% of the total valid votes.
Hence the 2nd candidate should have got 45% of the total valid votes
=> Valid votes that 2nd candidate got = total valid votes x
Answer: B) 2700
Answer: B
Question: In a basketball game, Dhoni scored 5 points more than Dravid, but only half as many points as Shewag. If the three players scored a combined total of 115 points, how many points did Dhoni score?
Options:
A)30
B)32
C)33
D)34
E)35
Rationale: Let Dravid scored point = x
Then Dhoni Scored = x+5
Shewag Scored = 2*(x+5) = 2x+10
As given, x+x+5+2x+10 = 115 points
4x+15 = 115
x = 115-15/4 = 25
So Dhoni Scored = x +15 i.e) 25+5 = 30
Answer : A
Answer: A
Question: A trader sells 40 metres of cloth for Rs.8200 at a profit of Rs.30 per metre of cloth. How much profit will the trder earn on 40 metres of cloth?
Options:
A)Rs.950
B)Rs.1500
C)Rs.1000
D)Rs.1200
E)None of these
Rationale: Explanation:
SP of 1 metre cloth = 8200/40 = Rs.205.
CP of 1 metre cloth = Rs.205 – 30 = Rs.175
CP on 40 metres = 175 x 40 = Rs.7000
Profit earned on 40 metres cloth = Rs.8200 – Rs.7000 = Rs.1200.
Answer: Option D
Answer: D
Question: What Is The Next Number
12 13 15 17 111 113 ?
Options:
A)154
B)220
C)129
D)428
E)117
Rationale: 117
These are the first 10 prime numbers (2, 3, 5...) prefixed with a 1
Answer : E
Answer: E
Question: A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:
Options:
A)250
B)330
C)352
D)253
E)163
Rationale: Let the middle digit be x.
Then, 2x = 10 or x = 5. So, the number is either 253 or 352.
Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit.
Hence, required number = 253.
ANSWER D
Answer: D
Question: When n is divided by 24, the remainder is 5. What is the remainder when 4n is divided by 8?
Options:
A)3
B)5
C)4
D)6
E)7
Rationale: Let n=5 (leaves a remainder of 5 when divided by 24)
4n = 4(5) =20, which leaves a remainder of 4 when divided by 8.
Answer C
Answer: C
Question: If a(a - 2) = 2 and b(b - 2) = 2, where a ≠ b, then a + b =
Options:
A) −1
B) −2
C) 4
D) 46
E) 48
Rationale: i.e. if a = -1 then b = 2
or if a = 2 then b = -1
But in each case a+b = -1+2 = -1
Answer: option A
Answer: A
Question: Find the value of x in 8.5 – { 5 ½ – [7 ½ + 2.8]/x}*4.25/(0.2)^2 = 306
Options:
A)3.2
B)3.4
C)3.5
D)4.1
E)4.2
Rationale: 8.5-{5.5-(7.5+(2.8/x))}*(4.25/0.04) = 306
 8.5-{5.5-{(7.5x+2.8)/x)}*(425/4) = 306
 8.5-{(5.5x-7.5x-2.8)/x}*(425/4) = 306
 8.5-{(-2x-2.8)/x}*106.25 = 306
 8.5-{(-212.5x-297.5)/x} = 306
 (306-221)x = 297.5  x =(297.5/85) = 3.5.
ANSWER C 3.5
Answer: C
Question: Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?
Options:
A)27:52
B)27:58
C)27:57
D)57:52
E)27:54
Rationale: 3h = 5c
6c = 10s
A = 21h*3 + 15c*2
= 63h + 30c
= 105c + 30c = 135c
B = 15c*6 + 40s*7 1/2
= 90c + 300s
= 90c + 180c = 270c
A:B = 135:270
27:52
Answer:A
Answer: A
Question: If m^(-1) = -1/7 then m^(-2) is equal to
Options:
A)-9
B)-3
C)-1/9
D)1/49
E)9
Rationale: You made a mistake here.
You're right till
m^-2 = 1/m^2 and m^-1 = 1/m^1 = 1/m
given m^-1 = -(1/7) so, 1/m = -(1/7) solving this, m = -7
Now, m^-2 = 1/m^2 = 1/(-7)^2 = 1/49 ANS D
Answer: D
Question: Martin buys a pencil and a notebook for 80 cents. At the same store, Gloria buys a notebook and an eraser for $1.05 cents, and Zachary buys a pencil and an eraser for 65 cents. How many cents would it cost to buy three pencils, three notebooks, and three erasers? (Assume that there is no volume discount.)
Options:
A)300
B)325
C)350
D)375
E)400
Rationale: pencil + notebook = 80
notebook + eraser = 105
pencil + eraser = 65
Let's add all three equations.
2 pencils + 2 notebooks + 2 erasers = 250 cents
The cost to buy 3 of each would be (3/2)(250) = 375
The answer is D.
Answer: D
Question: Visitors to show were charged Rs.15 each on the first day. Rs.7.50 on the second day, Rs.2.50 on the third day and total attendance on the three days were in ratio 2:5:13 respectively. The average charge per person for the whole show is?
Options:
A)2
B)9
C)5
D)8
E)3
Rationale: 2: 5: 13
2x 5x 13x
15 7.5 2.5
30x + 37.5x + 32.5x = 100x/20x
Average = 5
Answer: C
Answer: C
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.60000?
Options:
A)19860
B)3277
C)2688
D)2998
E)2789
Rationale: A = 60000(11/10)3
= 79860
= 60000
----------
19860
Answer:A
Answer: A
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is?
Options:
A)1/38
B)1/36
C)1/28
D)1/29
E)1/98
Rationale: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216
=1/36
Answer:B
Answer: B
Question: There are 6 working days in a regular week and for each day, the working hours are 10. A man earns Rs. 2.10 per hour for regular work and Rs. 4.20 per hour for overtime. If he earns Rs.525 in 4 weeks, how many hours did he work?
Options:
A)245
B)285
C)275
D)255
E)235
Rationale: Regular working hours in 4 weeks = (4 × 6 × 10) = 240 hours
Amount earned by working in these regular working hours
= 240 × 2.10 = Rs.504
Additional amount he earned = 525 - 504 = Rs.21
Hours he worked overtime = 21/4.2 = 210/42 = 5 hours
Total hours he worked = 240 + 5 = 245 hours
ANSWER:A
Answer: A
Question: A can do a piece of work in 3 hours; B and C together can do it in 2 hours, which A and B together can do it in 2 hours. How long will C alone take to do it?
Options:
A)2hours
B)5hours
C)6hours
D)4hours
E)3hours
Rationale: A's 1 hour work = 1/3;
(B + C)'s 1 hour work = 1/2;
(A + B)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/3 + 1/2) = 5/6
C's 1 hour work = (5/6 - 1/2) = 1/3
C alone will take 3 hours to do the work.
Answer:E
Answer: E
Question: A boy has 12 trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
Options:
A)120ways
B)149ways
C)144ways
D)130ways
E)100ways
Rationale: The boy can select one trouser in 12 ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 12 * 12
= 144 ways.
Answer: C
Answer: C
Question: A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 25km/hr. in return trip, he covers the same distance at an average speed of 20km/hr. the average speed of the car over the entire distance of 400 km is
Options:
A)8.95km/hr
B)22.2km/hr
C)27.8km/hr
D)37.9km/hr
E)8.45km/hr
Rationale: average speed = (2*25*20)/25+20 km/hr
=22.22 km/hr
Answer (B)
Answer: B
Question: A and B complete a job in 6 days. A alone can do the job in 9 days. If B works alone, how many days will it take to complete the job?
Options:
A)12
B)15
C)18
D)21
E)24
Rationale: The rate of A and B is 1/6
A's rate is 1/9
B's rate is 1/6 - 1/9 = 1/18
B can complete the job in 18 days.
The answer is C.
Answer: C
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good?
Options:
A)125/128
B)125/120
C)125/126
D)125/125
E)125/121
Rationale: Required probability = 1 - 1/126
= 125/126
Answer: C
Answer: C
Question: If x = 2, then what is the value of 8x √x3 – x2
Options:
A)32
B)34
C)88
D)37
E)91
Rationale: Explanation:
Given: x = 2
8 * 2 √23 – 22
16√8-4
16√4
16 * 2 = 32
ANSWER:A
Answer: A
Question: The volume of a cube is 1728 cc. Find its surface?
Options:
A)864
B)209
C)278
D)276
E)280
Rationale: a3 = 1728 => a = 12
6a2 = 6 * 12 * 12 = 864
Answer:A
Answer: A
Question: Ram is working on a set of Data Sufficiency problems for his December GMAT: a geometry problem, an algebra problem, and a data interpretation problem. He has determined that statement 1 of the geometry problem is insufficient on its own, that both statement 1 and 2 of the algebra problem are insufficient on their own, and that statement 2 of the data interpretation problem is insufficient on its own. If the probabilities are expressed as percents R, approximately how much greater is the probability that all three answers are “C” after Ram figures out that statement 1 of the data interpretation problem is also insufficient on its own?
Options:
A)R=2.3%
B)R=2.8%
C)R=3.3%
D)5.6%
E)8.3%
Rationale: Step 1: Figure out what we need to know.We have two probabilities that we need to figure out: the one before Raj figures out that statement 1 of the data interpretation problem is also insufficient, and the one after. The answer is the difference between them, in the form of a percent.
Step 2: The first probability.
If statement 1 of the geometry problem is insufficient, then the only valid answer choices are B, C, and E; the probability that it is C is 1/3.
If both statements of the algebra problem are insufficient on their own, then the only remaining valid answers are C and E; the probability that it is C is 1/2
If statement 2 of the data interpretation problem is insufficient, then the remaining answers are A, C, and E, and the probability that C is correct is 1/3.
The probability of all three occurring is the product of the probability fractions: (1/3)*(1/2)*(1/3) = 1/18.
Step 3: The second probability.
Only the third problem has changed; if Raj now knows that statement 1 is also insufficient, the valid answer choices are only C and E, leaving a 1/2 probability that the answer is C.
The probability of all three occurring is still the product of those fractions, but this time they are (1/3)*(1/2)*(1/2) = 1/12.
Step 4: The answer.Note that here, as will sometimes happen on the GMAT, values that you compute “along the way” appear as wrong answer choices. This problem calls for the difference between our two numbers, (1/12)-(1/18) = 1/36, which is a 2.77777% chance, rounded to 2.8% —the correct answer is Choice B.
Answer: B
Question: The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches?
Options:
A)31
B)66
C)88
D)99
E)12
Rationale: Total score of the batsman in 20 matches = 800.
Total score of the batsman in the next 10 matches = 130.
Total score of the batsman in the 30 matches = 930.
Average score of the batsman = 930/30 = 31.Answer:A
Answer: A
Question: Suppose in 1960, the consumer price index was 70 while in 2015 it is 280. What monthly salary in 2015 would have the same purchasing power as a monthly salary of 800 dollars in 1960?
Options:
A)2100
B)3200
C)2030
D)3000
E)None
Rationale: Solution:
Let x be the monthly salary in 2015.
x/800 =280/70
x × 70 = 280 × 800
70x = 224000
70/70 x= 224000/70
x = 3200
Answer B
Answer: B
Question: At Daifu university, 40% of all students are members of both a chess club and a swim team. If 20% of members of the swim team are not members of the chess club, what percentage of all Daifu students are members of the swim team?
Options:
A)20%
B)30%
C)40%
D)50%
E)60%
Rationale: Assume there are total of 100 students. 40 students are members of both clubs. We are told that: "20% of members of the swim team are not members of the chess club", thus if S is a # of members of the swim team then 0.2S is # of members of ONLY the swim teem:
40+0.2S=S --> S=50.
Answer: D.
Answer: D
Question: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?
Options:
A)2,145
B)6,435
C)12,100
D)12,870
E)25,740
Rationale: Total 3 letter passwords = 26 * 25 * 24 = 15600
Total letters = 26 = symmetrical letters (11) + asymmetrical letters (x) => x = 15
Total no. of 3 letters passwords using asymmetrical letters = 15 * 14 * 13 = 2730 (no repetition allowed)
Hence, no. of 3 letter passwords using atleast one symmetrical letter = 15600 - 2730 = 12870 ---> Option D
Answer: D
Question: 1,000^2 + 1,001^2 +1,002^2 + 1,003^2 + 1,004^2 + 1,005^2+ 1,006^2 =
Options:
A)6,030,053
B)6,030,054
C)6,030,055
D)6,042,091
E)6,030,057
Rationale: Interesting problem.
I think key is to notice that all the given answer choices differs in last two digits. Therefore, our entire focus should be to figure out how the given terms contribute to last two digits of total.
1000^2 -> 00
1001^1 -> 01
.
.
.
1006^2 -> 36
Total -> *91
Answer D.
Answer: D
Question: On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2.4% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?
Options:
A)2.04%
B)6.12%
C)8%
D)8.25%
E)10%
Rationale: If the interest were compounded annually instead of quarterly then in one year the interest would be 2.4*4=9.6%. Now, since the interest is compounded quarterly then there would be interest earned on interest (very small amount) thus the actual interest would be a little bit more than 9.6%,
Answer: E
Answer: E
Question: The center of a circle is (5, -1). (5, 7) is outside the circle, and (1, -1) is inside the circle. If the radius, r, is an
integer, how many possible values are there for r?
Options:
A) 3
B) 2
C) 6
D) 12
E) 1
Rationale: r must be greater than 4 and smaller than 8, hence r=5,6 or 7.
Answer C
Answer: C
Question: Nil and Ethan are brothers. They left their home
at the same time and drove to the same beach.
Nil drove at a speed of 50 miles per hour. Ethan
drove at a speed of 20 miles per hour. Nil
arrived at the beach 0.5 hour earlier than Ethan.
What is the distance between their home and the
beach?
Options:
A)60 miles
B)50 miles
C)40 miles
D)30 miles
E)20 miles
Rationale: Every hour, Nil gets ahead of Ethan 50 - 20 =
30 miles. When Nil arrived at the beach, Ethan
is only 20 × 0.5 = 10 miles behind. That tells us
they only drove 1 hour when Nil arrived at the
beach.
The distance between their home and the beach
is
Nil’s speed × Nil’s time
= 50 × 1 = 50 miles.
correct answer B
Answer: B