A Certain Computer Program Allows a User to Convert

Question

A certain computer program allows a user to convert a digital image in one of five formats—Formats V through Z—to other formats among Formats V through Z. An asterisk is shown at the intersection of a row and a column in the table if and only if the program can directly convert from the format indicated at the beginning of the row to the format indicated at the top of the column.

The program can also be used to perform a series of direct conversions to indirectly convert from one format to another. For example, the program cannot directly convert an image from Format V to Format W, but it can convert an image from Format V to Format X, and then from Format X to Format W.

For each of the following formats, select Can convert to every other format if the information provided indicates it is possible to convert, either directly or indirectly, from that format to each of the other four formats. Otherwise, select Cannot convert to one or more formats.

pking101 · Answer

can someone please help answer this.
This is a gmat prep official question.

SirSanguine · Answer

Hi pking101,

From the options we have to select "can be converted to all others or cannot" corresponding to each format.
First is format x..Look in the third row of the table x can be converted to only w directly, but then look in the second row where w can be further converted to any other format . Hence x can be indirectly converted too all other formats. Similarly  w can solve for other two questions. Hope this helps.

chetan2u · Answer

Actually, just scanning would let us get the answer. W : Check the row of W. There is an asterisk on all other formats, so W can convert to all other formats. Since W can convert to all, any format that can convert to W would also be able to convert to all other format. We can see that X can covert directly to W, so X can convert to all other indirectly. Now, we can say that since W and X can convert to all, any format that can convert to W and X would also be able to convert to all other format. Next, we can see that V, W and Y can convert to X. Hence, V and Y can also convert to all other indirectly. So, all of V, W, X and Y can convert to all other format, so if Z can convert to any one of them, it will also get converted to all other formats. Z can convert to Y. Hence, Z too can convert to all other indirectly. Solution: Yes for all GMAT-Club-Forum-6rtwazpy.png

lawyeroffduty · Answer

https://gmatclub.com/forum/download/file.php?id=82012

please let me know whether my thinking is right or not for format z, so format z can convert to y and then, format y can convert to format v and x, but not for format w, so in order to convert to format w, we can convert format y to format x and then format x to format w. and so, we get all the format for z. is my way of thinking right and method?

Bunuel · Answer

Yes, your thinking is right.

nandini14 · Answer

All three options from the table will indirectly form as wherever "*" is present that means it converts and checking the row of that letter we can figure out what all is included

egmat · Answer

Hi lawyeroffduty,

Yes, your thinking and method are exactly right! Let me confirm each step of your chain for Format Z.

From the table, Format Z can only directly convert to one format:
- Z → Y (direct, asterisk at row Z, column Y)

Now from Y, we check the table and see Y can directly convert to V, X, and Z:
- Z → Y → V (that gives us V)
- Z → Y → X (that gives us X)

But we still need W. As you correctly identified, Y cannot directly convert to W (no asterisk at row Y, column W). So we need one more step. Since we can get to X from Y, and X can directly convert to W (asterisk at row X, column W):
- Z → Y → X → W (that gives us W)

So the full picture from Format Z is:
- Z → Y (direct)
- Z → Y → V ( 2  steps)
- Z → Y → X ( 2  steps)
- Z → Y → X → W ( 3  steps)

All  four  other formats are reachable, so the answer is   Can Convert to every other format  .

Key Insight:  Your method of chaining conversions step by step is the  correct approach  for these questions.  The key idea is: whenever you cannot reach a format directly, look at what the intermediate formats you CAN reach are able to convert to, and keep extending the chain until you either reach every format or run out of new paths. You nailed it!

Harsh_ · Answer

Using table
 FROM --> TO

(1) X --> W --> V
 X --> W --> Y
 X --> W --> Z
 Can Convert to every other format

(2) Y --> V
 Y --> X --> W
 Y --> Z
 Can Convert to every other format

(3) Z --> Y --> V
 Z --> Y --> X --> W
 Can Convert to every other format

A Certain Computer Program Allows a User to Convert

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Can Convert to every other format	cannot convert to every other format
		Format X
		Format Y
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A Certain Computer Program Allows a User to Convert

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