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One red bottle and five blue bottles are to be arranged in a straight line from left to right on a windowsill. How many

Problem Solving

One red bottle and five blue bottles are to be arranged in a straight line from left to right on a windowsill. How many

One red bottle and five blue bottles are to be arranged in a straight line from left to right on a windowsill. How many different, unique arrangements are possible?

A. $6$
B. $12$
C. $30$
D. $60$
E. $120$

The OA is A

by BTGmoderatorLU: Thu May 08, 2025 6:13 pm; Forum: Problem Solving; Topic: One red bottle and five blue bottles are to be arranged in a straight line from left to right on a windowsill. How many; Replies: 0; Views: 338

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When cleaning her house, Carlotta discovered an old box of candles and figurines, each of which is unique. She wants to

Data Sufficiency

When cleaning her house, Carlotta discovered an old box of candles and figurines, each of which is unique. She wants to

When cleaning her house, Carlotta discovered an old box of candles and figurines, each of which is unique. She wants to display the items on a shelf. How many different ways can she place the items in a row on the shelf if she alternates between candles and figurines? 1) If only the figurines were l...

by BTGmoderatorLU: Thu May 08, 2025 6:03 pm; Forum: Data Sufficiency; Topic: When cleaning her house, Carlotta discovered an old box of candles and figurines, each of which is unique. She wants to; Replies: 0; Views: 16

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How many $3$-digits numbers satisfy the following conditions: The first digit is different from zero and all digits

Problem Solving

How many $3$-digits numbers satisfy the following conditions: The first digit is different from zero and all digits

How many $3$-digit numbers satisfy the following conditions: The first digit is different from zero, and all digits are different from each other?

A. $504$
B. $576$
C. $648$
D. $672$
E. $810$

The OA is C

by BTGmoderatorLU: Thu May 08, 2025 5:43 pm; Forum: Problem Solving; Topic: How many $3$-digits numbers satisfy the following conditions: The first digit is different from zero and all digits; Replies: 0; Views: 32

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A salesperson gets a $15\%$ commission on each sale he makes. How many sales of $\$270$ each must he make in order

Problem Solving

A salesperson gets a $15\%$ commission on each sale he makes. How many sales of $\$270$ each must he make in order

A salesperson gets a $15\%$ commission on each sale he makes. How many sales of $\$270$ each must he make in order to reach a salary of at least $\$1000?$

A. $15$
B. $24$
C. $25$
D. $26$
E. $52$

The OA is C

by BTGmoderatorLU: Thu May 01, 2025 5:20 am; Forum: Problem Solving; Topic: A salesperson gets a $15\%$ commission on each sale he makes. How many sales of $\$270$ each must he make in order; Replies: 0; Views: 486

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The temperature of a place at noon on a certain day is $25\%$ higher than the temperature of the same place at

Data Sufficiency

The temperature of a place at noon on a certain day is $25\%$ higher than the temperature of the same place at

The temperature of a place at noon on a certain day is $25\%$ higher than the temperature of the same place at midnight on the same day. What is the temperature of the place at midnight? 1) The temperature of the place at midnight is $20\%$ lower than the temperature of the same place at noon 2)...

by BTGmoderatorLU: Thu May 01, 2025 4:56 am; Forum: Data Sufficiency; Topic: The temperature of a place at noon on a certain day is $25\%$ higher than the temperature of the same place at; Replies: 0; Views: 169

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A person who has a certain amount with him goes to market. He can buy $50$ oranges or $40$ mangoes. He retains

Problem Solving

A person who has a certain amount with him goes to market. He can buy $50$ oranges or $40$ mangoes. He retains

A person who has a certain amount with him goes to market. He can buy $50$ oranges or $40$ mangoes. He retains $10\%$ of the amount for taxi fares and buys $20$ mangoes and of the balance he purchases oranges. Number of oranges he can purchase is A. $10$ B. $15$ C. $20$ D. $25$ E. \(...

by BTGmoderatorLU: Thu May 01, 2025 4:43 am; Forum: Problem Solving; Topic: A person who has a certain amount with him goes to market. He can buy $50$ oranges or $40$ mangoes. He retains; Replies: 0; Views: 54

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If Hollis’s gross hourly pay is increased by $\$2$ per hour, how many fewer hours per week could Hollis work to earn

Data Sufficiency

If Hollis’s gross hourly pay is increased by $\$2$ per hour, how many fewer hours per week could Hollis work to earn

If Hollis’s gross hourly pay is increased by $\$2$ per hour, how many fewer hours per week could Hollis work to earn the same gross weekly pay that she currently receives for working $40$ hours per week? 1) A pay increase of $\$2$ per hour will result in a new gross hourly pay that is $10/9$...

by BTGmoderatorLU: Wed Apr 23, 2025 3:36 pm; Forum: Data Sufficiency; Topic: If Hollis’s gross hourly pay is increased by $\$2$ per hour, how many fewer hours per week could Hollis work to earn; Replies: 0; Views: 282

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Marie earned $\$0.75$ for every mile she walked in a charity walkathon. If she earned a total of $\$18.00$ at that

Problem Solving

Marie earned $\$0.75$ for every mile she walked in a charity walkathon. If she earned a total of $\$18.00$ at that

Marie earned $\$0.75$ for every mile she walked in a charity walkathon. If she earned a total of $\$18.00$ at that rate, how many miles did she walk?

A. $13.5$
B. $17.5$
C. $21$
D. $22.5$
E. $24$

The OA is E

by BTGmoderatorLU: Wed Apr 23, 2025 3:27 pm; Forum: Problem Solving; Topic: Marie earned $\$0.75$ for every mile she walked in a charity walkathon. If she earned a total of $\$18.00$ at that; Replies: 0; Views: 182

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In a park, there are owners accompanied with atleast one pet dog. Total head count of dogs and owners is $90$ and

Problem Solving

In a park, there are owners accompanied with atleast one pet dog. Total head count of dogs and owners is $90$ and

In a park, there are owners accompanied with atleast one pet dog. Total head count of dogs and owners is $90$ and there total leg count is $270.$ How many owners and dogs are there in the park? A. $21$ Owners, $69$ Dogs B. $30$ Owners, $60$ Dogs C. $33$ Owners, $54$ Dogs D. $39$ Ow...

by BTGmoderatorLU: Wed Apr 23, 2025 3:03 pm; Forum: Problem Solving; Topic: In a park, there are owners accompanied with atleast one pet dog. Total head count of dogs and owners is $90$ and; Replies: 0; Views: 148

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Is the slope of Line $L > 0?$

Data Sufficiency

Is the slope of Line $L > 0?$

Is the slope of Line $L > 0?$

1. Line $L$ does NOT pass through Quandrant III
2. Line $L$ has positive $Y$-intercept

The OA is A

by BTGmoderatorLU: Fri Apr 11, 2025 5:37 am; Forum: Data Sufficiency; Topic: Is the slope of Line $L > 0?$; Replies: 0; Views: 1810

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A triangle $ABC$ has area $32$ sq units and its side $BC,$ of length $8$ units, lies on the line $x = 4.$ Then

Problem Solving

A triangle $ABC$ has area $32$ sq units and its side $BC,$ of length $8$ units, lies on the line $x = 4.$ Then

A triangle $ABC$ has area $32$ sq units and its side $BC,$ of length $8$ units, lies on the line $x = 4.$ Then the shortest possible distance between $A$ and the point $(0,0)$ is

A. $2$
B. $2\sqrt{2}$
C. $4$
D. $4\sqrt{2}$
E. $6$

The OA is C

by BTGmoderatorLU: Fri Apr 11, 2025 5:12 am; Forum: Problem Solving; Topic: A triangle $ABC$ has area $32$ sq units and its side $BC,$ of length $8$ units, lies on the line $x = 4.$ Then; Replies: 0; Views: 392

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Line $L$ passes through the points $A$ and $B$ having coordinates $(p,q)$ and $(r,s),$ respectively. Is the

Data Sufficiency

Line $L$ passes through the points $A$ and $B$ having coordinates $(p,q)$ and $(r,s),$ respectively. Is the

Line $L$ passes through the points $A$ and $B$ having coordinates $(p,q)$ and $(r,s),$ respectively. Is the slope of Line $L$ positive?

1. $p < 0$ and $q < 0$
2. $r > 0$ and $s < 0$

The OA is E

by BTGmoderatorLU: Fri Apr 11, 2025 4:59 am; Forum: Data Sufficiency; Topic: Line $L$ passes through the points $A$ and $B$ having coordinates $(p,q)$ and $(r,s),$ respectively. Is the; Replies: 0; Views: 487

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Perpendicular lines $m$ and $n$ intersect at point $(a, b),$ where $a > b > 0.$ The slope of line $m$ is

Problem Solving

Perpendicular lines $m$ and $n$ intersect at point $(a, b),$ where $a > b > 0.$ The slope of line $m$ is

Perpendicular lines $m$ and $n$ intersect at point $(a, b),$ where $a > b > 0.$ The slope of line $m$ is between $0$ and $1.$ Which of the following statements MUST be true? I. The $x$-intercept of line $n$ is positive II. The product of the $x$ and $y$-intercepts of line $m$...

by BTGmoderatorLU: Fri Apr 11, 2025 4:51 am; Forum: Problem Solving; Topic: Perpendicular lines $m$ and $n$ intersect at point $(a, b),$ where $a > b > 0.$ The slope of line $m$ is; Replies: 0; Views: 312

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In an $xy$-coordinate system, which point lies in the interior of a circle with center $(0,0)$ and radius $3?$

Problem Solving

In an $xy$-coordinate system, which point lies in the interior of a circle with center $(0,0)$ and radius $3?$

In an $xy$-coordinate system, which point lies in the interior of a circle with center $(0,0)$ and radius $3?$

A. $(1, −3)$
B. $(−1, −2)$
C. $(−3,1)$
D. $(0,3)$
E. $(3,3)$

The OA is B

by BTGmoderatorLU: Sat Apr 05, 2025 5:36 am; Forum: Problem Solving; Topic: In an $xy$-coordinate system, which point lies in the interior of a circle with center $(0,0)$ and radius $3?$; Replies: 0; Views: 341

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In the $xy$-plane, the circle $C$ centered at the origin $O$ is intersected by a line $l$ at two points $A$

Data Sufficiency

In the $xy$-plane, the circle $C$ centered at the origin $O$ is intersected by a line $l$ at two points $A$

In the $xy$-plane, the circle $C$ centered at the origin $O$ is intersected by a line $l$ at two points $A$ and $B.$ A line from $O$ is drawn to $AB$ intersecting $AB$ at point $D,$ such that the product of the slopes of $OD$ and $AB$ is $-1.$ If the line $l$ does not pas...

by BTGmoderatorLU: Sat Apr 05, 2025 5:28 am; Forum: Data Sufficiency; Topic: In the $xy$-plane, the circle $C$ centered at the origin $O$ is intersected by a line $l$ at two points $A$; Replies: 0; Views: 451

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