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Lines AD, BE and CF are parallel to each other such that lines p and q are transversal to these lines. Line p intersects AD, BE and CF at X, Y and Z respectively while line q intersects them at L, M and N respectively. If XY : XZ = 2 : 3 and LM = 4 units, MN = ?
  • a)
    2 units
  • b)
    3 units
  • c)
    1.5 units
  • d)
    1 unit
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Lines AD, BE and CF are parallel to each other such that lines p and q...
AD, BE and CF are parallel lines and p and q are the transversals
► XY / YZ = LM / MN
► XY : XZ = 2 : 3
► XY / YZ = 2 / 1 = LM / MN
► LM = 4
► MN = 4/2 = 2 units
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Most Upvoted Answer
Lines AD, BE and CF are parallel to each other such that lines p and q...
Given:
- Lines AD, BE, and CF are parallel to each other.
- Lines p and q are transversal to these lines.
- Line p intersects AD, BE, and CF at X, Y, and Z respectively.
- Line q intersects them at L, M, and N respectively.
- XY : XZ = 2 : 3
- LM = 4 units

To find: MN = ?

Solution:
Given that AD, BE, and CF are parallel lines, we can conclude the following:

Corresponding angles:
- ∠AXY = ∠LMN (since XY || LM and p and q are transversals)
- ∠BYZ = ∠MNL (since YZ || MN and p and q are transversals)
- ∠CZX = ∠NLM (since XZ || NL and p and q are transversals)

Using the property of ratios in similar triangles, we can equate the ratios of corresponding sides:

Since XY : XZ = 2 : 3, we can assume that XY = 2x and XZ = 3x, where x is a constant.
Similarly, we can assume that LM = 4y, where y is a constant.

Since XY || LM and p and q are transversals, we can conclude that triangle AXY and triangle LXM are similar triangles.

Using the property of ratios in similar triangles, we can equate the ratios of corresponding sides:

AX/LX = XY/LM
AX/4y = (2x)/4y
AX/LX = 2/4
AX/LX = 1/2

Similarly, we can conclude that triangle BYZ and triangle MNL are similar triangles:

BY/MN = YZ/ML
BY/MN = (3x)/4y
BY/MN = 3/4
BY/MN = 3/4

Given that LM = 4 units, we can conclude that MN = (4 * 4) / 3, which simplifies to 16/3 units.

Therefore, the value of MN is 16/3 units, which can be approximated as 5.33 units.

Hence, the correct answer is option A) 2 units.
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Legrand Casino recently purchased a slot machine; a gaming machine, which had the main unit and five sub-units, labeled as Alpha, Gamma, Beta, Theta and Omega. The main, as well as each of the sub-units, had five slots, labeled as Red, Blue, Grey, Black, and Yellow. The game with this slotting machine involved punching the right coin in the right slot in the right sequence i.e. one after another. For example, if coin number 3 is punched into slot Blue in Gamma sub-unit and if the main unit also pushes the coin to Blue slot, then the punch is said to be a winning shot. If the coin in the sub-unit is punched into the right slot when compared to the corresponding coin in the main unit, then the player gets Rs. 1,000 as reward. On the other hand, if the slots do not match then the player loses Rs. 333. Each player gets 25 coins to play.However, after a couple of days, this slotting machine developed a peculiar problem. In the sub-units irrespective of the slot you intended to put in the coin, the sub-unit pushed the coin into the slot it wanted to every time on its own.To find out which slots in the sub-units had developed the snag, the technician played on all the sub-units using 25 coins in each of the sub-units.After some kind of analysis he found that the main machine and each of the sub-units could identify right slots for 15 coins, however for the balance of 10 coins listed below, each of the sub-units assumed different positions as right slots when compared to the main unit whose allocation of slots was the benchmark for performance of other sub-units.On playing with these sub-units, the technician earned Rs. 17,000, Rs. 11,660, Rs. 18,330, Rs. 14,330 and Rs. 18,330 respectively from each of Alpha, Gamma, Beta, Theta and Omega. All the amount being rounded off to previous tens figure. Of the ten slots which had developed the snag, there was at least one sub-unit which identified the right slot for exactly 9 of the 10 slots.The table below gives the slots identified by each of the sub-units as right slots for the 10 problematic coins.What is the median value of the number of incorrect slots individually identified by the 5 sub-units?

Legrand Casino recently purchased a slot machine; a gaming machine, which had a main unit and five sub-units, labeled as Alpha, Gamma, Beta, Theta and Omega. The main as well as each of the sub-units had five slots, labeled as Red, Blue, Grey, Black and Yellow. The game with this slotting machine involved punching the right coin in the right slot in the right sequence i.e. one after another. For example, if coin number 3 is punched into slot Blue in Gamma sub-unit and if the main unit also pushes the coin to Blue slot, then the punch is said to be a winning shot. If the coin in the sub-unit is punched into the right slot when compared to the corresponding coin in the main unit, then the player gets Rs. 1,000 as reward. On the other hand, if the slots do not match then the player loses Rs. 333. Each player gets 25 coins to play.However, after a couple of days this slotting machine developed a peculiar problem. In the sub-units irrespective of the slot you intended to put in the coin, the sub-unit pushed the coin into the slot it wanted to every time on its own.To find out which slots in the sub-units had developed the snag, the technician played on all the sub-units using 25 coins in each of the sub-units.After some kind of analysis he found that the main machine and each of the sub-units could identify right slots for 15 coins, however for the balance of 10 coins listed below, each of the sub-units assumed different positions as right slots when compared to the main unit whose allocation of slots was the benchmark for performance of other sub-units.On playing with these sub-units, the technician earned Rs. 17,000, Rs. 11,660, Rs. 18,330, Rs. 14,330 and Rs. 18,330 respectively from each of Alpha, Gamma, Beta, Theta and Omega. All the amount being rounded off to previous tens figure. Of the ten slots which had developed the snag, there was atleast one sub-unit which identified the right slot for exactly 9 of the 10 slots.The table below gives the slots identified by each of the sub-units as right slots for the 10 problematic coins.Q. Which of these can never be a valid combination of correctly slotted coin numbers for the Alpha sub-unit?

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Lines AD, BE and CF are parallel to each other such that lines p and q are transversal to these lines. Line p intersects AD, BE and CF at X, Y and Z respectively while line q intersects them at L, M and N respectively. If XY : XZ = 2 : 3 and LM = 4 units, MN = ?a)2 unitsb)3 unitsc)1.5 unitsd)1 unitCorrect answer is option 'A'. Can you explain this answer?
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Lines AD, BE and CF are parallel to each other such that lines p and q are transversal to these lines. Line p intersects AD, BE and CF at X, Y and Z respectively while line q intersects them at L, M and N respectively. If XY : XZ = 2 : 3 and LM = 4 units, MN = ?a)2 unitsb)3 unitsc)1.5 unitsd)1 unitCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Lines AD, BE and CF are parallel to each other such that lines p and q are transversal to these lines. Line p intersects AD, BE and CF at X, Y and Z respectively while line q intersects them at L, M and N respectively. If XY : XZ = 2 : 3 and LM = 4 units, MN = ?a)2 unitsb)3 unitsc)1.5 unitsd)1 unitCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Lines AD, BE and CF are parallel to each other such that lines p and q are transversal to these lines. Line p intersects AD, BE and CF at X, Y and Z respectively while line q intersects them at L, M and N respectively. If XY : XZ = 2 : 3 and LM = 4 units, MN = ?a)2 unitsb)3 unitsc)1.5 unitsd)1 unitCorrect answer is option 'A'. Can you explain this answer?.
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