divelab/Sys2Bench huggingface dataset:
Question: In measuring the sides of a rectangle, one side is taken 8% in excess, and the other 7% in deficit. Find the error percent in the area calculated from these measurements.
Options:
A)0.11%
B)0.7%
C)0.44%
D)0.6%
E)0.8%
Rationale: Let x and y be the sides of the rectangle. Then, Correct area = xy.
Calculated area = (27/25) x (40/43) y = (913/909 )(xy)
Error In measurement = (913/909)xy- xy = (4/909)xy
Error percentage = [(4/909)xy (1/xy)100] % = (11/25) % = 0.44%.
Answer is C.
Answer: C
Question: __2A
x__B
____
CC
In the multiplication problem above, A, B, and C represent distinct digits. If the sum of A and B is equal to 4.6, what is the value of C?
Options:
A)6
B)5.2
C)4
D)3
E)2
Rationale: If A+B=4.6
assuming A and B are positive then A*B<10 (they could be either 1,2,3,4)
therefore
A*B=C
2*B=C
A+B=4.6
Three simple equations - divide the 1st/2nd --> A=2 plug it the 3rd --> B=2.6 --> C=5.2 (ANSWER B)
Answer: B
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
Options:
A)6 cm
B)4 cm
C)8 cm
D)3 cm
E)9 cm
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h = (4/3)π (12)3 => h
= 9 cm
Answer:E
Answer: E
Question: A train 420 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)36 sec
B)16 sec
C)17 sec
D)88 sec
E)12 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 420 * 2/35 = 36 sec
Answer:A
Answer: A
Question: If a square mirror has a 20-inch diagonal, what is the approximate perimeter T of the mirror, in inches?
Options:
A) 40
B) 60
C) 80
D) 100
E) 120
Rationale: if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other.
And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter T must be less than 80, so we can eliminate answer choice C, D and E.
so Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A.
Now we are left with is B
Answer: B
Question: In a T.V. factory, an average of 60TVs are produced per day for the fist 25days of the months. A few workers fellill for the next five daysreducing the daily avg for the month to58 sets/day . The average production per day for day last 5days is ?
Options:
A)35
B)39
C)48
D)50
E)52
Rationale: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 60
= 240
∴ Average for last 5 days = 240 / 5
= 48
C
Answer: C
Question: A certain company had a total annual expenditure of 1.89∗10^7 on employee salaries last year. If the company employed 420 people, what was the average employee salary?
Options:
A)$20,000
B)$25,000
C)$35,000
D)$40,000
E)$45,000
Rationale: Given: Total annual expenditure of 1.89∗10^7 on employee salaries
Total employees = 420
Observe that 420*4 = 1890
Therefore try to bring the numerator in terms of 1890
Average salary = (1890*10^4) /420 = 4.5*10^4 = 45,000
Option E
Answer: E
Question: Which of the following must be an integer if the integer x is divisible by both 18 and 24?
Options:
A)x/252
B)x/189
C)x/126
D)x/108
E)x/72
Rationale: the integer has to be multiple of LCM of 18 and 24, which is 72..
so x/126 will be an integer
ans E
Answer: E
Question: Factory X's bulbs work for over 5000 hours in 78% of cases, whereas factory Y's bulbs work for over 5000 hours in 65% of cases. It is known that factory X supplies 90% of the total bulbs available. What is the chance that a purchased bulb will work for longer than 5000 hours?
Options:
A)76.4%
B)76.7%
C)77.4%
D)75%
E)73.9%
Rationale: For X, 90% of 78% will work.
For Y, 10% of 65% will work. *10% is the rest of the bulb supply in the market.
So, the probability that a purchased bulb will work is:
0.90(0.78) = .702
0.10(0.65) = 0.065
The combined probability then is 70.2 + 6.5 = 76.7%
ANS B
Answer: B
Question: Positive Integer A gives the remainder of 32 when divided by another positive Integer B. If A/B = 147.64, what is the value of B?
Options:
A)96
B)75
C)48
D)50
E)12
Rationale: .64 of B = Remainder
.64 of B = 32
B = (32 *100) / 64= 50.
D
Answer: D
Question: There are three motor's are available in the office,namely P,Q,& R.Its power consumption is different.Ratio of the power consumption of 3 different motor's 3:4:5.Total power consumption of 3 motor's are 1250 units.Then find out the power consumption of motor R?
Options:
A)655.50 UNITS
B)258.54 UNITS
C)566.29 UNITS
D)520.84 UNITS
E)634.25 UNITS
Rationale: Ratio of the power consumption of 3 different motor's 3+4+5=12.
Power consumption of motor R= 5/12*1250 = 520.84 UNIT Answer: D
Answer: D
Question: There is a total of 90 marbles in a box, each of which is red, green, blue, or white. If one marble is drawn from the box at random, the probability that it will be white is 1/3 and the probability that it will be green is 1/5. What is the probability that the marble will be either red or blue?
Options:
A)1/3
B)3/5
C)7/15
D)11/30
E)17/30
Rationale: P(red or blue) = 1 - P(white) - P(green) = 15/15 - 5/15 - 3/15 = 7/15
The answer is C.
Answer: C
Question: A can finish a work in 18days and B can do the same work in half the time taken by A. Then, working together what part of the same work they can finish in a day?
Options:
A)1/2
B)1/3
C)1/6
D)2/5
E)2/9
Rationale: 1days work of A+B = (18+9)/18*9 = 1/6
Answer is C
Answer: C
Question: The perimeter of one face of a cube is 24 cm. Its volume will be:
Options:
A)216cm3
B)400cm3
C)250cm3
D)625cm3
E)None of these
Rationale: Explanation:
Edge of cude = 24/4 = 6 cm
Volume = a*a*a = 6*6*6 = 216 cm cube
Option A
Answer: A
Question: There is a single elimination checkers tournament, meaning when one player loses, they are out of the tournament. There are 50 players in the tournament, how many games are played?
Options:
A)49
B)25
C)20
D)10
E)5
Rationale: A
The number of games always adds up to one less than the number of players in a single elimination tournament. You may calculate it any way. Therefore, 49 games were played.
Answer: A
Question: 7 people sit at the round table. In how many ways can we sit them so that Bob and Bill don't sit opposing each other?
Options:
A)A)400
B)B)420
C)C)440
D)D)460
E)E)480
Rationale: 7 People: Bob,Bill,Red,Blue,White,Pink,Purple
Round Table: T
7 Chairs: 1,2,3,4,5,6,7
Let chairs 1 and 4 be opposite each other;
Bob is sitting on 1 and Bill is sitting on 4;
The rest of the people on 2,3,5,6,7 - can rearrange themselves in 5! ways
Now, Bill and Bob swap their positions;
Bob is sitting on 4 and Bill is sitting on 1;
The rest of the people on 2,3,5,6,7 - can rearrange themselves in 5! ways
Thus total number of ways in which Bob and Bill are sitting opposite each other = 2*5! = 120*2 = 240
We have to find in how many ways they are NOT sitting opposite; subtract 240 from the total number of possible arrangements;
In circular permutation, Total number of arrangements of n people = (n-1)!
Here number of people = 7
Arrangements = (7-1)! = 6!= 720
Number of ways Bob and Bill are NOT sitting opposite = 720-240 = 480.
Answer: E
Answer: E
Question: Ram professes to sell his goods at the cost price but he made use of 850 grms instead of a kg, what is the gain percent?
A. 11%
Options:
A)11 1/9%
B)11 1/8%
C)17.65%
D)11 5/9%
E)11 1/5%
Rationale: 850 --- 150
100 --- ? => 17.65%
Answer:C
Answer: C
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Options:
A)8%
B)7%
C)10%
D)12%
E)4%
Rationale: Option E
Explanation:
65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer: E
Question: In a city, the streets are aligned in a grid, where the east-west roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The north-south roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 8th Rd and 7th Ave in the shortest possible time, how many different routes could he take?
Options:
A)150
B)180
C)210
D)240
E)270
Rationale: Bills needs to walk 6 blocks north and 4 blocks east.
One possible solution is NNNNNNEEEE.
There are 10C6 = 210 possible solutions.
The answer is C.
Answer: C
Question: A tailor trims 4 feet from opposite edges of a square piece of cloth, and 3 feet from the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?
Options:
A)18
B)20
C)24
D)26
E)40
Rationale: Let the original side of the square be x.
(x-8)*(x-6) = 120 = 10*12
x = 18
The answer is A.
Answer: A
Question: 62467 × 9998 = ?
Options:
A)624545037
B)627745452
C)624545077
D)624545066
E)625454211
Rationale: D
624545066
62467 × 9998 = 62467 × (10000 - 2)
= 62467 × 10000 - 62467 × 2
= 624670000 - 124934
= 624545066
Answer: D
Question: A car travels 25 km an hour faster than a bus for a journey of 500 km. If the bus takes 10 hours more than the car, then the speeds of the bus and the car are
Options:
A)25 km/h and 40 km/h, respectively
B)25 km/h and 60 km/h, respectively
C)25 km/h and 50 km/h, respectively
D)25 km/h and 70 km/h, respectively
E)None of these
Rationale: Let the speed of the bus be x km / h.
Then speed of the car = (x + 25) km / h
∴ 500/x=500/x+25+10
⇒ x2 + 25x – 1250 = 0 ⇒ x = 25
Thus, speed of the bus = 25 km/h
Speed of the car = 50 km/h
Answer C
Answer: C
Question: This topic is locked. If you want to discuss this question please re-post it in the respective forum.
If y ≠ 3 and 3r/y is a prime integer greater than 2, which of the following must be true?
I. r = y
II. y = 1
III. r and y are prime integers.
Options:
A) None
B) I only
C) II only
D) III only
E) I and III
Rationale: 3r/y and if r=y then ans is 3 and 3 is prime number, which is greater than 2. so ans must be B. Please post OA.
Answer: A
Question: In May Mrs Lee's earnings were 90 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?
Options:
A)92
B)35
C)64
D)46
E)355
Rationale: Lets say the Family Income is 100
In May, lee earned 90Family income is 10
In june, Lee earned 20% more than May, so it is (90+20*90/100 = 108)
Family Income is same 10
In June Lee's Income percent is 108*100/118 ~ 92
Ans is A
Answer: A
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 5 years at 50% per annum is Rs.200 of money?
Options:
A)1256
B)2000
C)3600
D)8400
E)4566
Rationale: P = 200(100/50)5 => P = 2000
Answer: B
Answer: B
Question: Three carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if two of the carpenters work together at their respective rates ?
Options:
A)11/15
B)3/5
C)11/30
D)47/90
E)5/9
Rationale: Farmer A, B, C, and D
A's rate: 1/3 job/hour
B's rate: 1/4 job/hour
C's rate: 1/5 job/hour
D's rate: 1/7 job/hour
By intuition we know that the three fastest farmers are A B and C.
As such
(1/3 + 1/4 + 1/5)*(2/3) = ?
47/90 or (D)
Answer: D
Question: A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
Options:
A)Rs. 45
B)Rs. 50
C)Rs. 55
D)Rs. 60
E)Rs. 40
Rationale: A : B : C = (10 x 7) : (12 x 5) : (15 x 3) = 70 : 60 : 45 = 14 : 12 : 9.
C's rent = Rs. (175 x9/35) = Rs. 45.
THE CORRECT ANSWER IS A.
Answer: A
Question: Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 1/2 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
Options:
A)2/5
B)1/3
C)4/13
D)8/29
E)6/33
Rationale: Now ultimately the speed of every machine is given with respect to Mach O.
So lets assume the speed of O, say 12 hrs to make x units (assuming 6 because we can see we will need to divide by 3 and 4
Mach O makes x units in 12 hrs
So, Mach N = 1/2 of O = 1/2*12 = 6 hrs to make x units
and Mach M = 3/4 of N = 3/4*6 = 6 hrs to make x units
No they are running simultaneously. Lets see how much each mach makes in 1 hr
Mach O = x/12 units
Mach N = x/6 units
Mach M = x/6 units
In 1 hr, together they make - x/12+x/6+x/6 = 5x/12
So what ratio of this has Mach N made?
(x/6) / (5x/12) = 2/5
Ans:A=2/5
Answer: A
Question: A polling company reports that there is a 80% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z?
Options:
A)10
B)16
C)6
D)4
E)5
Rationale: 80% - Candidate Elected
100%-60% = 40% - Candidate doesnotsigh Bill X
50% - Candidate randomly chooses between two bills.
These are multiplicative:
80% x 40% x 50%
0.8 x 0.4 x 0.5 = 0.16 = 16%
Answer (B)
Answer: B
Question: Find the least number of complete years in which a sum of money put out at 25% compound interest will be more than double of itself?
Options:
A)6 years
B)7 years
C)9 years
D)4 years
E)1 years
Rationale: 4 years
Answer: D
Answer: D
Question: Last year, for every 100 million vehicles that travelled on a certain highway, 92 vehicles were involved in accidents. If 3 billion vehicles travelled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000)
Options:
A)288
B)320
C)2,760
D)3,200
E)28,800
Rationale: To solve we will set up a proportion. We know that “100 million vehicles is to 92 accidents as 3 billion vehicles is to x accidents”. To express everything in terms of “millions”, we can use 3,000 million rather than 3 billion. Creating a proportion we have:
100/92 = 3,000/x
Cross multiplying gives us:
100x = 3,000 * 92
x = 30 * 92 = 2,760
Correct answer is C.
Answer: C
Question: Using all the letters of the word "THURSDAY", how many different words can be formed?
Options:
A)8
B)8!
C)7!
D)7
E)5
Rationale: Total number of letters = 8
Using these letters the number of 8 letters words formed is ⁸P₈ = 8!.
Answer:B
Answer: B
Question: If n = 2×3×5×7×11×13×17x19, then which of the following statements must be true?
I. n2 is divisible by 600
II. n + 19 is divisible by 19
III. is even n+4 / 2 = even
IV . n is divisible 35.
Options:
A)I only
B)b- II only
C)III only
D)I and III only
E)none and IV only
Rationale: n = 2×3×5×7×11×13×17x19=9699690
I. n2 is not divisible by 600
II. n + 19 is not divisible by 19
III. is even n+4 / 2 = odd
IV . n is divisible 35.
E
Answer: E
Question: Which of the following are/is prime?
I. 143
II. 145
III. 149
Options:
A) II only
B) III only
C) III
D) IIII
E) I, II,III
Rationale: 1) 143 = 13*11 so we know it is not prime quickly eliminate all options having 1 as a choice
which leaves us with 2 ) and 3) as possible answers
From here on we find 147 = 3* 49 so we eliminate 147 which leaves us with 149 as the only possible solution
A
Answer: A
Question: In a school of 900 students, 44% wear blue shirts, 28% wear red shirts, 10% wear green shirts, and the remaining students wear other colors. How many students wear other colors (not blue, not red, not green)?
Options:
A)144
B)153
C)162
D)171
E)180
Rationale: 44 + 28 + 10 = 82%
100 – 82 = 18%
900 * 18/100 = 162
The answer is C.
Answer: C
Question: Irin, Ingrid and Nell bake chocolate chip cookies in the ratio of 9.18: 5.17: 2.05. If altogether they baked a batch of 148 cookies, what percent of the cookies did Ingrid bake?
Options:
A)0.125%
B)1.25%
C)31.33%
D)125%
E)0.152%
Rationale: 9.18x+5.17x+2.05x = 16.4x = 150 cookies
x= 150/16.4 = 9.14 (approx)
So, Ingrid baked 9.14*5.17 cookies or 47cookies (approx)
% share = 47/150 = 31.33 approx
Hence, answer is C.
Answer: C
Question: 5301 x 13 =?
Options:
A)68381
B)69831
C)68931
D)68319
E)68913
Rationale: Append 0 before and after: 053010
Calculation:
1 x 3 + 0 = 3 (take 3 as ones digit of the product)
0 x 3 + 1 = 1 (take 1 tens digit of the product)
3 x 3 + 0 = 9 (take 9 hundreds digit of the product)
5 x 3 + 3 = 18 (take 8 as thousands digit of the product, carry over 1)
0 x 3 + 5 = 5; 5 + 1 = 6 (take 6 as ten thousands digits of the product)
So, 5301 x 13 = 68913
Answer is E.
Answer: E
Question: hoose the number pair/group which is different from others.
1. 40 : 50
2. 30 : 36
3. 8 : 10
4. 28 : 35
5. 16 : 20
Options:
A)30 : 36
B)30 : 39
C)30 : 332
D)30 : 37
E)30 : 34
Rationale: Explanation:
40 : 50 ==> 4 : 5
30 : 36 ==> 5 : 6
8 : 10 ==> 4 : 5
28 : 35 ==> 4 : 5
16 : 20 ==> 4 : 5
In each of the pair except 30 : 36, the ratio of the two numbers is 4 : 5.
ANSWER: A
Answer: A
Question: A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleble and there are 14 unsaleable mangoes in the crate then how msny mango are there in the crate?
Options:
A)100 mangoes
B)110 mangoes
C)120 mangoes
D)130 mangoes
E)140 mangoes
Rationale: 140 mangoes
ANSWER:E
Answer: E
Question: A can do a piece of work in 5 days of 9 hours each and B alone can do it in 5 days of 3 hours each.how long will they take it to do working together
2 1/4 hours a day?
Options:
A)2 days
B)3 days
C)4 days
D)5 days
E)6 days
Rationale: A's work per hour=1/45
B's work per hour=1/15
A & B's work per hour together=(1/45)+(1/15)=4/45
so a & B together complete the work in 45/4 hours...
if they work 2 1/4=9/4 hours a day,
it will take (45/4)/(9/4) days=5 days...
ANSWER:D
Answer: D
Question: The first year, two cows produced 8100 litres of milk. The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year. How many litres were milked from each cow each year?
Options:
A)4370, 4730 liters and 3800, 4300 liters
B)4300, 3800 liters and 4730, 3800 liters
C)4730, 3800 liters and 4300, 3800 liters
D)3800, 4300 liters and 4370, 4730 liters
E)4300, 4370 liters and 3800, 4730 liters
Rationale: Let x be the amount of milk the first cow produced during the first year. Then the second cow produced (8100−x) litres of milk that year. The second year, each cow produced the same amount of milk as they did the first year plus the increase of 15% or 10%.
So 8100+15100⋅x+10100⋅(8100−x)=9100
Therefore 8100+320x+110(8100−x)=9100
120x=190
x=3800
Therefore, the cows produced 3800 and 4300 litres of milk the first year, and 4370 and 4730 litres of milk the second year, respectively.
So answer is D.
Answer: D
Question: one bottle is half-full of oil and another bottle with twice the capacity is one quarter full of oil. if water is added so that both the bottles are full and the contents of both are then poured into a third bottle that is empty and large enough to hold the contents of both, what fractions of the contents in the third bottle is oil?
Options:
A)1/4
B)1/3
C)3/8
D)2/3
E)1/2
Rationale: Let assume that 1st bottle capacity = 1Litre;
Therefore, it contain 1/2 litre Oil and 1/2 litre water .
(i.e) Water = 1/2 litre
Oil = 1/2 litre
2nd bottle is twice the capacity
i.e. 2 litre capacity
It means, 1/2litre filled with oil and 1(1/2)litre filled with water.
i.e. Oil = 1/2 liter
Water = 1(1/2)litre
In total the third bottle will contain,
1 litre oil and 2 litre water.
i.e., Oil = 1 litre
Water = 2 liter
Therefore, oil proportion is 1/3
ANSWER:B
Answer: B
Question: The perimeter of a semi circle is 144 cm then the radius is?
Options:
A)22
B)28
C)99
D)77
E)21
Rationale: 36/7 r = 144 => r = 28
Answer: B
Answer: B
Question: A furniture manufacturer has two machines, but only one can be used at a time. Machine E is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine E can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?
Options:
A)14
B)13
C)11
D)9
E)7
Rationale: machine E finish the job in 2*12 shifts = 24 shifts
machine B finish the job in 2*15 shifts = 30 shifts
Lets assume total work require 120 shifts
Therefore,
rate of E = 5 shifts/day
rate of B = 4 shifts/day
rate of (E+B) = 9 shifts/day
According to current schedule work complete in a day = 5+4+(9/2) =13.5 shifts/day
Therefore, Time required to finish 120 shifts = (120/13.5) = 8.88.. days ~ 9 days=D
Answer: D
Question: 9+2+2^2+2^3+2^4+2^5=？
Options:
A)(2^3-1)(2^3+1)
B)2^6+1
C)2^5-1
D)2^6+7
E)2^5-2
Rationale: From 9+2+2^2+2^3+2^4+2^5=71,
2^6+7=71
the correct answer is D.
Answer: D
Question: A salesmanâ€™s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 800 more than that by the previous schema, his sales were worth?
Options:
A)s. 4,000
B)s. 12,000
C)s. 30,000
D)s. 40,000
E)s. 50,000
Rationale: [1000 + (X-4000) * (2.5/100)] - X * (5/100) = 800
X =4000
ANSWER:A
Answer: A
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12400 after a year?
Options:
A)3630
B)3637
C)3720
D)3631
E)3635
Rationale: 6300:4200:10500
3:2:5
3/10 * 12400 = 3720
Answer: C
Answer: C
Question: A man invested Rs.1552 in a stock at 97 to obtain an income of Rs.128. What is the dividend from the stock?
Options:
A)None of these
B)9.7%
C)7.5%
D)8%
E)8.5%
Rationale: Explanation :
By investing Rs.1552, income = Rs.128
By investing Rs.97, income = 128×97/1552=8
ie, dividend = 8%
Answer : Option D
Answer: D
Question: I. a2 + 8a + 16 = 0,
II. b2 - 4b + 3 = 0 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)2 = 0 => a = -4
II.(b - 3)(b - 1) = 0
=> b = 1, 3 => a < b
Option A
Answer: A
Question: A certain fruit stand sold apples for $0.80 each and bananas for $0.70 each. If a customer purchased both apples and bananas from the stand for a total of $7.30, what total number of apples and bananas did the customer purchase?
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: Let's start with 1 apple for $0.80.
Let's subtract $0.80 from $7.30 until we get a multiple of $0.70.
$7.30, $6.50, $5.70, $4.90 = 7*$0.70
The customer purchased 7 bananas and 3 apples.
The answer is B.
Answer: B
Question: A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options:
A)16.5%
B)20%
C)35%
D)55%
E)65%
Rationale: In my view easiest method would be, eliminating the percentage sign
Let 3.5 be 35
5.5 be 55
and 3 be 30
then first eq: S+F=E
130S+155F=135E
5s=20F
therefore, s=4F and then E=5F
F/E=F/5F=20%
Therefore, Answer is B
Answer: B
Question: If integer k is equal to the sum of all even multiples of 35 between 280 and 630, what is the greatest prime factor of k?
Options:
A)5
B)7
C)11
D)13
E)11*455
Rationale: if we break down what the stem is asking what is the sum of all mult of 30 between 300 and 600.
using arithmetic progression to find n : 630 =280+ (n - 1) 35
350+ 35 = 35n
385 = 35n => n = 11
the sum would be: 11* mean
mean = [630 + 280] / 2 = 455
11*455 =
E
Answer: E