divelab/Sys2Bench huggingface dataset:
Question: A letter lock consists of five rings each marked with three different letters. The number of distinct unsuccessful attempts to open the lock is at the most?
Options:
A)277
B)269
C)242
D)177
E)123
Rationale: Since each ring consists of three different letters, the total number of attempts possible with the five rings is
= 3 * 3 * 3 * 3 * 3 = 216. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts = 243 - 1
= 242
Answer:C
Answer: C
Question: It takes 3 workers a total of 9 hours to build a giant machine with each worker working at the same rate. If 3 workers start to build the machine at 11:00 AM, and one extra worker per hour is added beginning at 2:00 PM, at what time will the machine be complete?
Options:
A)5:15
B)5:26
C)5:37
D)5:48
E)5:59
Rationale: 3 workers build 1/9 of a machine in one hour.
1 worker builds 1/27 of a machine in one hour.
In the first 3 hours, 3 workers build 3*(1/27)*3=9/27 of a machine
From 2:00 to 3:00, 4 workers build another 4/27. The total is 13/27.
From 3:00 to 4:00, 5 workers build another 5/27. The total is 18/27.
From 4:00 to 5:00, 6 workers build another 6/27. The total is 24/27.
To build another 3/27, 7 workers need (3/7)*60 minutes which is about 26 minutes.
The machine is complete at about 5:26.
The answer is B.
Answer: B
Question: Indu gave Bindu Rs.3750 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
Options:
A)s.6
B)s.2
C)s.5
D)s.3
E)s.4
Rationale: 3750 = D(100/4)2
D = 6
ANSWER:A
Answer: A
Question: Of the five numbers in a sequence, the first term is 10,000, and each of the following terms is 60% of the previous term. What is the value range of the five numbers?
Options:
A)8,704
B)9,750
C)9,975
D)9,984
E)10,736
Rationale: 1st number= 10,000
2nd number = 60% of 10,000= 6000
3rd number= 60% of 6000= 3600
4th number = 60% of 3600= 2160
5th number= 60% of 2160= 1296
Range = 10,000-1296= 8704
A is the answer
Answer: A
Question: A property decreases in value every year at the rate of 6 1/4% of its value at the beginning of the year its value at the end of 3 years was Rs.21093. Find its value at the beginning of the first year?
Options:
A)25600.24
B)25600.28
C)25600.243
D)25600.21
E)25600.23
Rationale: 6 1/4% = 1/16
x *15/16 * 15/16 * 15/16 = 21093
x = 25600.24
Answer: A
Answer: A
Question: Five years ago, John’s age was half of the age he will be in 8 years. How old is he now?
Options:
A)14years
B)15years
C)16years
D)17years
E)18years
Rationale: Let John=j,j-5=(j+8)/2,then j=18years
ANSWER:E
Answer: E
Question: 9. On level farmland, two runners leave at the same time from the intersection of two country roads. One runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 2 miles per hour slower than the first runner's rate. How far apart, to the nearest mile, will they be after 1/2 hour ?
Options:
A) 5
B) 7
C) 8
D) 12
E) 14
Rationale: If runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle.
Side 1 = 8 m/h --> 4 m in 1/2 hr
Side 2 = 6 m/h --> 3 m in 1/2 hr
to complete this right angle triangle
d^2 = 4^2 + 3^2
d^2 = 25
= 5
Answer option A
Answer: A
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 1/7. What is the probability that they agree in stating the same fact?
Options:
A)18/35
B)18/38
C)18/36
D)18/16
E)15/35
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability
= 3/5 * 1/7 + 2/5 * 6/7
= 3/35 + 12/35
= 15/35
Answer: E
Answer: E
Question: Given a square of length 2m. Its corners are cut such that to represent a regular octagon. Find the length of side of octagon
Options:
A)2
B)3
C)4
D)5
E)7
Rationale: Let x is the side of the octagon and x + 2y is the side of the square.
In the given octagon, y2+y2=x2⇒2y2=x2⇒y=x2–√y2+y2=x2⇒2y2=x2⇒y=x2
But x2–√+x+x2–√=2x2+x+x2=2
⇒2–√x+x=2⇒2x+x=2
⇒x=22–√+1=22–√+1×2–√−12–√−1=2(2–√−1)⇒x=22+1=22+1×2−12−1=2(2−1)
Answer:A
Answer: A
Question: If the selling price is quintupled,the profit is hexatrupled,what is the percentage of profit??
Options:
A)50%
B)100%
C)150%
D)200%
E)250%
Rationale: we can make two equations from the given info..
let selling price be S and cost price be C..
so profit=P=S-C...
if S is doubled profit is tripled..
so 6P=5S-C..
or S=5P...
therefore C=P..
% of profit=P/P=100%
B
Answer: B
Question: How many different 6 digit numbers can be formed from the number 745698 by re-arranging its digits so that the odd digits occupy even position
Options:
A)15
B)12
C)8
D)7
E)36
Rationale: There are 3 odd numbers which have to be placed at 3 even places =3!=6 ways
There are 3 even numbers which have to be placed at 3 odd places. So 3! = 6ways
so total number of ways of arranging all these numbers are 6 * 6= 36 ways
Answer:E
Answer: E
Question: A car traveled from San Diego to San Francisco at an average speed of 45 miles per hour. If the journey back took twice as long, what was the average speed of the trip?
Options:
A)30.
B)32.
C)36.
D)42.
E)44.
Rationale: Let the time taken be = x
One way distance = 45x
Total distance traveled = 2 * 45x = 90x
Total time taken = x + 2x = 3x
Average speed = 90x/3x = 30
Answer: A
Answer: A
Question: In how many no. between 100 and 1000 at least one of their digits is 7?
Options:
A)900
B)648
C)720
D)252
E)729
Rationale: Let's count the number of occurrences with only one 7:
(1) 7XX: 1 * 9 * 9 = 81
(2) X7X: 8 * 1 * 9 = 72
(3) XX7: 8 * 9 * 1 = 72
81 + 72 + 72 = 225
At this point we can already see that the answer must be D since the choice are very dispersed.
Anyways, let's count number of occurrences with two 7s:
(1) 77X: 1 * 1 * 9 = 9
(2) X77: 8 * 1 * 1 = 8
(3) 7X7: 1 * 9 * 1 = 9
9 + 8 + 9 = 26
Number 777 is missing. So the total becomes
225 + 26 + 1 = 252
D is the correct answer.
Answer: D
Question: 1,236
1,263
1,326
.....
....
+6,321
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,3,6 exactly once in each integer. What is the sum of these 24 integers?
Options:
A)63,332
B)67,772
C)71,112
D)75,552
E)79,992
Rationale: In each of the units, tens, hundreds, and thousands place, each digit will appear 6 times.
Then the sum equals 6(1111)+6(2222)+6(3333)+6(6666) = 79,992
The answer is E.
Answer: E
Question: The total number of students in Grades 1 and 2 is 30 more than the total number of students in grades 2 and 5. How much lesser is the number of students in Grade 5 as compared to Grade 1?
Options:
A)20
B)30
C)10
D)40
E)15
Rationale: (Grade 1 + Grade 2) - (Grade 2 + Grade 5) = 30
Grade 1 - Grade 5 = 30
Answer: B
Answer: B
Question: One card is drawn at random from a pack of 48 cards. What is the probability that the card drawn is a face card?
Options:
A)1/4
B)1/7
C)1/8
D)1/5
E)2/5
Rationale: Clearly, there are 52 cards, out of which there are 12 face cards.
P (getting a face card) =	12/48 = 1/4
A
Answer: A
Question: A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
Options:
A)50
B)45
C)20
D)73
E)27
Rationale: A+B+C = 500
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 500
----------------
C = 50
Answer:A
Answer: A
Question: Kelly and Jody packed boxes with books. If Jody packed 20% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number that Jody packed?
Options:
A)1 to 6
B)4 to 1
C)2 to 5
D)3 to 5
E)2 to 3
Rationale: Explanation:
If Jody packed 20% of the boxes then Kelly packed 80%. The ratio of the number of boxes Kelly packed to the number Jody packed is thus 80%/20%=4/1
Answer: Option B
Answer: B
Question: 8k8
+ k88
--------
1,6y6
If k and y represent non-zero digits within the integers above, what is y?
Options:
A)6
B)7
C)8
D)9
E)17
Rationale: 8k8
k88
--------
16y6
Trial and error or just plug-in method might be the shortest way to solve this problem. Though you can narrow down the possible values of k to just two: 7 and 8 --> 8**+7**=16** or 8**+8**=16** (k can not be less than 7 or 9, as the result won't be 16**). After that it's easy to get that k=7 and y=6.
Answer: A.
Answer: A
Question: A and B partner in a business. A contribute 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B's money was used?
Options:
A)5 months
B)10 months
C)8 months
D)12 months
E)7 months
Rationale: B received 2/3 of the profit.
Then A received remaining 1/3 of the profit.
=> A : B =1/3:2/3=1:2
Let the total capital =x
Then A's capital =x4
B's capital =x–x/4=3x/4
Assume B's money was used for b months
Then A:B =x/4×15:3x/4×b
⇒15x/4:3bx/4=1:2
⇒15:3b=1:2
⇒5:b=1:2
⇒5×2=1×b
⇒b=10
Answer is B.
Answer: B
Question: I. a2 - 2a - 8 = 0,
II. b2 = 9 to solve both the equations to find the values of a and b?
Options:
A)If a < b
B)If a ≤ b
C)If the relationship between a and b cannot be established
D)If a > b
E)If a ≥ b
Rationale: Explanation:
I. (a - 4)(a + 2) = 0
=> a = 4, -2
II. b2 = 9
=> b = ± 3
-2 < 3, -2 > -3, 4 > 3, 4 > -3,
No relation can be established between a and b.
C)
Answer: C
Question: A, B and C can do a work in 7 days, 8 days and 12 days respectively. In how many days can all three of them working together, complete the work?
Options:
A)2 50/59
B)2 5/59
C)2 2/50
D)2 2/59
E)2 1/59
Rationale: Work done by all three of them in one day = 1/7 + 1/8 + 1/12 = 59/168
The number of days required = 168/59 = 2 50/59 days.
Answer:A
Answer: A
Question: Five bells commence tolling together and toll at intervals of 2, 4, 6, 8,10 seconds respectively. In 60 minutes, how many times do they toll together?
Options:
A)41
B)10
C)31
D)16
E)17
Rationale: L.C.M of 2,4,6,8,10 is 240. i.e after each 2 min they will toll together.So in 60 min they will toll 30 times.As they have initially tolled once,The answer will be 30+1=31.
ANSWER:C
Answer: C
Question: In a school with 5 classes, each class has 2 students less than the previous class. How many students are there in the largest class if the total number of students at school is 100?
Options:
A)24
B)25
C)26
D)27
E)28
Rationale: Let x be the number of students in the largest class.
Then x + (x-2) + (x-4) + (x-6) + (x-8) = 100
5x -20 = 100
5x = 120
x = 24
The answer is A.
Answer: A
Question: A wheel that has 6 cogs is meshed with a larger wheel of 7 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is:
Options:
A)9
B)10
C)6
D)18
E)7
Rationale: Explanation :
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
7:6::21:x => 7 * x = 21 * 6
=> x = (21 * 6)/7
=> x = 18
Answer : D
Answer: D
Question: 0.009/x=0.1. find the value of X
Options:
A)0.0009
B)0.09
C)0.9
D)9
E)90
Rationale: x=0.009/0.1=0.09
ANSWER:B
Answer: B
Question: If 36 men can do a piece of work in 25 hours, in how many hours will 10 men do it?
Options:
A)22
B)38
C)60
D)88
E)90
Rationale: Explanation:
Let the required no of hours be x. Then
Less men , More hours (Indirect Proportion)
\inline \fn_jvn \therefore 10:36 ::25:x \inline \fn_jvn \Leftrightarrow (10 x X)=(36 x 25) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 25}{10}=90
Hence, 10 men can do it in 90 hours.
Answer: E) 90
Answer: E
Question: w, b, c, and d are positive integers. If the remainder is 9 when w is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d?
Options:
A) 20
B) 19
C) 18
D) 16
E) 15
Rationale: When w is divided by b remainder is 9 that means b is greater than or equals to 10, similarly d is greater than or equals to 6.
b + d cannot be 15, hence E is the answer.
Answer: E
Question: Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 19 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel?
Options:
A)54
B)57
C)60
D)36
E)96
Rationale: B
57
It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 19 MPH = 57 miles
Answer: B
Question: On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ?
Options:
A)5
B)7
C)9
D)11
E)12
Rationale: Formula: (Divisor*Quotient) + Remainder = Dividend.
Soln:
(56*Q)+29 = D -------(1)
D%8 = R -------------(2)
From equation(2),
((56*Q)+29)%8 = R.
=> Assume Q = 1.
=> (56+29)%8 = R.
=> 85%8 = R
=> 5 = R.
A)
Answer: A
Question: Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
Options:
A)5
B)7
C)9
D)11
E)13
Rationale: Explanation:
x – y = 5
4x – 6y = 6
x = 12 y = 7
B)
Answer: B
Question: If YWVSQ is 25 - 23 - 21 - 19 - 17, Then MKIGW
Options:
A)13 - 11 - 9 - 7 - 9
B)13 - 11 - 9 - 7 - 6
C)13 - 11 - 9 - 7 - 11
D)13 - 11 - 9 - 7 - 3
E)13 - 11 - 9 - 7 - 1
Rationale: MKIGW = 13 - 11 - 9 - 7 - 11
Note: this is a dummy question. Dont answer these questions
Answer:C
Answer: C
Question: What is the value of (5!*4!*3!*2/ 6!*6!)-1/15?
Options:
A)5
B)12
C)20
D)0
E)4
Rationale: (5!*4!*3!*2/6!*6!)-1/15
(5!*4!*3!*2/5!*6*4!*5*6)-1/15
(3!*2/6*5*6)-1/15
1/15-1/15=0
answer D
Answer: D
Question: A worker's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 6 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
Options:
A)1/6
B)1/5
C)1/4
D)1/3
E)1/2
Rationale: Let x be the fraction of her take-home pay that the worker saved.
Let P be the monthly pay.
12xP = 6(1-x)P
12xP = 6P - 6xP
18xP = 6P
x = 1/3
The answer is D.
Answer: D
Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 1800 interest only for the period. The principal amount borrowed by him was:
Options:
A)s. 2,500
B)s. 1,000
C)s. 15,000
D)s. 5,000
E)s. 2,000
Rationale: Principal = Rs. (100 x 1800)/(12X3) = Rs. 5000. Answer: Option D
Answer: D
Question: Find the amount on Rs.5000 in 2 years, the rate of interest being 10% per first year and 12% for the second year?
Options:
A)3377
B)6160
C)5460
D)1976
E)1671
Rationale: 5000 * 110/100 * 112/100 => 6160
Answer: B
Answer: B
Question: What is the greatest value of n such that 18^n is a factor of 18! ?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: We know that 18 = 2 *3^2.
Hence, we need to find total number of 3s in 18! ( As out of 3 and 2 , we will have count of 3 least)
No. of 3s = 18/3 = 6/3 = 2.
Add the numbers in Bold, you will get total number of 3s = 8.
Hence, total number of 3^2 = 8/2 = 4.
Hence, answer is 4.
ANSWER:D
Answer: D
Question: In 1992 a total of 100 earthquakes occurred worldwide, some but not all of which occurred in Asia. If 10 of these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?
Options:
A)1/5
B)1/9
C)1/2
D)1/3
E)1/4
Rationale: We're given a couple of facts to work with:
1) There were a total of 100 earthquakes
2) Of those earthquakes, 10 of them occurred in Asia
We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.
Thus, there were 90 earthquakes that DID NOT occur in Asia....
The answer to the question is 10/90 = 1/9
Answer : B
Answer: B
Question: How many such 6's are there in the following number series which are followed by an even number and preceded by any odd number ? 3 6 4 5 7 6 3 5 4 3 6 4 5 6 4 1 6 3 9 6 3 4 5 6
Options:
A)three
B)one
C)two
D)four
E)none
Rationale: 3 6 4
3 6 4
5 6 4
so three times
ANSWER:A
Answer: A
Question: A train leaves Delhi at 11 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?
Options:
A)360
B)288
C)600
D)888
E)121
Rationale: D = 30 * 3 = 90
RS = 40 – 30 = 10
T = 90/10 = 9
D = 40 * 9 = 360 km
Answer: A
Answer: A
Question: In a family 11 people eat only vegetarian, 6 people eat only non veg., 9 people eat both veg and non veg.. How many people eat veg in the family?
Options:
A)20
B)11
C)9
D)31
E)21
Rationale: Total people eat veg = only veg + both veg and non veg
Total= 11+9= 20
Answer = A
Answer: A
Question: 30 pens and 75 pencils were purchased for 450. If the average price of a pencil was 2.00, find the average price of a pen.
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: Since average price of a pencil = 2
∴ Price of 75 pencils = 150
∴ Price of 30 pens = (450 – 150) = 300
∴ Average price of a pen = 360⁄60 = 10
Answer A
Answer: A
Question: A, Band C enter into partnership. A invests 3 times as much as B and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 8800. What is the share of B ?
Options:
A)1100
B)800
C)1400
D)1200
E)1600
Rationale: Let C's capital = Rs. x. Then, B's capital = Rs. (2/3)x
A’s capital = Rs. (3 x (2/3).x) = Rs. 2x.
Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3.
Hence, B's share = Rs. ( 8800 x (2/11))= Rs. 1600.
Answer is E
Answer: E
Question: A car covers a distance of 624 km in 4 hours. Find its speed?
Options:
A)104
B)277
C)156
D)269
E)213
Rationale: 624/4 = 156 kmph
Answer:C
Answer: C
Question: Shop Offered 32% offer for every Shirt, Smith bought a shirt at Rs. 650. and What was the shop's original selling Price?
Options:
A)955
B)550
C)600
D)700
E)750
Rationale: SP* (68/100) = 650
SP= 9.55 * 100 => CP = 955
Answer:A
Answer: A
Question: A Booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 m3. The emptying capacity of the tank is 10 m3 per minute higher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?
Options:
A)18
B)50
C)34
D)69
E)59
Rationale: Let, the filling capacity of the pump be x m3/min
Then, emptying capacity of the pump=(x+10) m3/min.
So,2400/x – 2400/(x+10) = 8
on solving x=50.
ANSWER:B
Answer: B
Question: If 0.75 : x :: 5 : 8, then x is equal to:
Options:
A)120
B)12
C)1.2
D)0.12
E)0.012
Rationale: ((x) x 5) = (0.75 x 8)
= x = 6/5
= 1.20
Answer is C.
Answer: C
Question: If a student loses 5 kilograms, he will weigh twice as much as his sister. Together they now weigh 116 kilograms. What is the student's present weight in kilograms?
Options:
A)76
B)77
C)78
D)79
E)80
Rationale: Let x be the weight of the sister.
Then the student's weight is 2x+5.
x + (2x+5) = 116
3x = 111
x = 37 kg
Then the student's weight is 79 kg.
The answer is D.
Answer: D
Question: A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 25%, what should be the sale price of the mixed tea?
Options:
A)23.75
B)22
C)20
D)19.20
E)None of these
Rationale: C.P. of mixture = 80×15+20×20/80+20=16
∴ S.P. = (100+25)/100×16=20
Answer C
Answer: C
Question: If x = 1 + √2, then what is the value of x4 - 4x3 + 4x2 + 5?
Options:
A)-1
B)0
C)6
D)2
E)3
Rationale: Answer
x = 1 + √2
∴ x4 - 4x3 + 4x2 + 5 = x2(x2 - 4x + 4) + 5
= x2(x - 2)2 + 5
= (1 + √2)2(1 + √2 - 2)2 + 5
=(√2 + 1)2 (√2 - 1)2 + 5
=[(√2)2 - (1)2]2 + 5
=(2 - 1)2 =1 + 5=6
Correct Option: C
Answer: C
Question: When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now?
Options:
A)42 years
B)41 years
C)43 years
D)40 years
E)45 years
Rationale: Let x= current age 4(x+4)+5(x+5)=10x ;so x=R 41 years
Answer C
Answer: C
Question: If one-third of one-fourth of a number is 15, then three-tenth of that number is:
A. 35
Options:
A)23
B)87
C)26
D)54
E)01
Rationale: Explanation:
The number is 1/3 of 1/4 is =15 then 1/3 × 1/4 = 15
Number is 180 then 180 × 3/10 = 54
Answer: D
Answer: D
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 15 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)5 days
B)6 days
C)7 days
D)8 days
E)9 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 Ã— 15/25 = 6 days.
B)
Answer: B
Question: In a garden, there are 10 rows and 15 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is
Options:
A)20 m
B)30 m
C)24 m
D)26 m
E)28 m
Rationale: Explanation:
Each row contains 15 plants.
There are 14 gapes between the two corner trees (14 x 2) metres and 1 metre on each side is left.
Therefore Length = (28 + 2) m = 30 m.
Answer: B
Answer: B
Question: If x and y are integers and x + y = 5, which of the following must be true?
Options:
A)x and y are consecutive integers.
B)If x < 0, then y > 0.
C)If x > 0, then y < 0.
D)Both x and y are even.
E)Both x and y are less than 5.
Rationale: Notice that the question asks which of the following MUST be true, not COULD be true.
Given: x + y = 5
A. x and y are consecutive integers: not necessarily true, for example x=1 and y=4;
B. If x < 0, then y > 0: if x is negative then y must be positive in order x+y to be positive, so this statement must be true;
C. If x > 0, then y < 0: not necessarily true, for example x=1 and y=4;
D. Both x and y are even: never true, as the sum of two even numbers is even and can not equal to odd number 5;
E. Both x and y are less than 5: not necessarily true, for example x=6 and y=-1;
Answer: B.
Answer: B
Question: Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 5 miles to Red Rock, retraced his path back for 2 miles, and then ran 3 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n?
Options:
A)1 ≤ n ≤23
B)3 ≤ n ≤21
C)6 ≤ n ≤18
D)5 ≤ n ≤19
E)9 ≤ n ≤15
Rationale: ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+5-2+3=18 for the maximum, and 12-5+2-3=6 for the minimum, so C is the answer
Answer: C
Question: 8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the water is 16 : 65. How much wine the cask hold originally ?
Options:
A)18 litres of wine
B)24 litres of wine
C)32 litres
D)42 litres
E)None
Rationale: Solution
Let the quantity of the wine in the cask originally be x litres
then, quantity of wine left in cask after 4 operations
= [x(1- 8/x)4] litres.
Therefore x(1- 8/x)4 / x = 16/81 =› (1- 8/x)4 = (2/3)2
=› (x - 8 / x) = 2/3 =› 3x - 24 = 2x =› x = 24.
Answer B
Answer: B
Question: The sides of a cube are in the ratio 1:2 the ratio of their volume is?
Options:
A)1:6
B)1:4
C)1:0
D)1:2
E)1:1
Rationale: 1:4
Answer:B
Answer: B
Question: It takes a boat 3 hours to travel down a river from point A to point B, and 5 hours to travel up the river from B to A. How long would it take the same boat to go from A to B in still water?
Options:
A)1h 15m
B)6h 35m
C)3h 45m
D)2h 49m
E)4h 40m
Rationale: Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B.
d = 3(S + r) : boat traveling down river
d = 5(S - r) : boat traveling up river
3(S + r) = 5(S - r)
r = S / 4 : solve above equation for r
d = 3(S + S/4) : substitute r by S/4 in equation B
d / S = 3.75 hours = 3 hours and 45 minutes.
correct answer is :C) 3h 45m
Answer: C