# Social Distancing with Data Sufficiency Challenge! – Day 30

Congratulations!!! You made in through our 30-Day Data Sufficiency Challenge! This is the last post in this series (but certainly won’t be my last post about DS!)

This series was designed to help you step up your Data Sufficiency practice while we all spend a little extra time at home during the coronavirus situation. If you missed any of the previous questions, click on the tag “Social Distancing DS Challenge” at the bottom of this post to see all of the questions in this series!

**Question #30**

A 40-foot long platform connects two adjacent buildings, and the platform is made up of a one-plank-wide strip of square-shaped planks. How many planks comprise the platform?

(1) Each plank has a diagonal of 5√2 feet.

(2) Each plank has a width of 5 feet.

**Explanation**

Statement (1) is sufficient because we can determine that the square-shaped planks have sides of length 5. 8 square planks of length 5 would make a 40-foot long sidewalk. Remember that the diagonal of a square is length * √2.

Statement (2) provides the same information as Statement 1, and knowing the width (or length) of each plank will tell you the total number of planks needed to make up the total platform.

The correct answer is (D).

# Social Distancing with Data Sufficiency Challenge! – Day 29

*This series is designed to help you step up your Data Sufficiency practice while we all spend a little extra time at home during the coronavirus situation; I’m going to publish one practice Data Sufficiency question each day! You can choose to do all of them, or none of them. *

*Click on the tag “Social Distancing DS Challenge” at the bottom of this post to see all of the questions in this series! *

*And remember to take whatever precautions you need to stay healthy over the next few weeks! *

**Question #29**

Is *n* equal to 7 ?

(1) *n* ≥ 7

(2) *n* ≤ 7

**Explanation**

Since each statement, considered independently, merely provides a range that extends infinitely in one direction (greater in statement 1, less than in statement 2), either of these statements taken alone is not sufficient. Combined, however, we can declare the following range for *n*: 7 ≤ *n* ≤ 7, which is equivalent to *n* = 7. The correct answer is (C).

# Social Distancing with Data Sufficiency Challenge! – Day 28

*This series is designed to help you step up your Data Sufficiency practice while we all spend a little extra time at home during the coronavirus situation; I’m going to publish one practice Data Sufficiency question each day! You can choose to do all of them, or none of them. *

*Click on the tag “Social Distancing DS Challenge” at the bottom of this post to see all of the questions in this series! *

*And remember to take whatever precautions you need to stay healthy over the next few weeks! *

**Question #28**

The interior of a rectangular box is 54 inches long, 27 inches wide, and 9 inches high. The box is filled with *x *cylindrical tubes of tennis balls that stand upright in rows and columns such that all the cylinders are touching and there is no additional space for extra tubes. If the tubes are 9 inches high, what is the value of *x*?

(1) 18 tubes fit exactly along the interior length of the box.

(2) Each of the tubes has a diameter of 3 inches.

**Explanation**

With statement (1), we can determine *x* by finding the diameter of each tube. We know the length is 54 inches. If 18 tubes fit along that edge, we know the diameter is: ^{54}/_{18} = 3 We can then figure out that ^{27}/_{3} = 9 tubes would fit along the width. And from there, we can determine *x* (but to save time, we won’t work out the math). Sufficient.

And statement (2) gives us the diameter outright, and we already know we can find *x* using the diameter with the given dimensions. Sufficient. The correct answer is (D).

# Social Distancing with Data Sufficiency Challenge! – Day 27

*And remember to take whatever precautions you need to stay healthy over the next few weeks! *

**Question #27**

Jeff wants to organize the first 15 marbles of his marble collection on a shelf that is x centimeters wide. The marbles vary in diameter. Will the 15 marbles fit on the shelf space if they are arranged side-by-side?

(1)* x* = 30 centimeters

(2) The first 20 marbles in the collection have an average diameter of 2 centimeters.

**Explanation**

Statement (1) tells us nothing about the marbles, so it can’t be sufficient, and statement (2) doesn’t mention the width of the shelf (value of *x*), so it can’t be sufficient, either.

But what about combining them? Not so fast: even though the average in statement (2) would accommodate the 15 marbles on the 30cm shelf, the average applies to the first 20 marbles rather than the first 15. It’s possible that the first ten marbles each have a diameter of 3cm, but the second ten each have a diameter of 1cm. The first ten alone would take up the full 30cm, leaving no room for marbles 11-15.

Thus, we cannot be sure the first 15 have an average diameter of 2 or less. The correct answer is (E).

# Social Distancing with Data Sufficiency Challenge! – Day 26

*And remember to take whatever precautions you need to stay healthy over the next few weeks! *

**Question #26**

What is the value of *ab + bc* ?

(1) *b *= 5

(2) *a + c *= 8

**Explanation**

Statement (1) is not sufficient to answer the question. If we substitute in the given value, we can see that we still know nothing about* a* and *c*.

Statement (2) gives us the info we need about* a* and *c*. Lack of info about *b* makes this answer alone also not sufficient.

But before we think about the statements combined, let’s simplify the given information: *ab + bc* = *b(a + c)*. Now looking at the statements in conjunction, we can get to the value by substituting in the given values in the statements. The correct answer is (C).

# Social Distancing with Data Sufficiency Challenge! – Day 25

*And remember to take whatever precautions you need to stay healthy over the next few weeks! *

**Question #25**

The production costs for the printing of greeting cards increases, though not proportionally, with the number of greeting cards printed. Did the production costs exceed $5 million in the printing of 700,000 greeting cards?

(1) The production costs exceeded $2.5 million in the printing of 400,000 greeting cards.

(2) The production costs exceeded $6 million in the printing of 600,000 greeting cards.

**Explanation**

With statement (1), if production costs increased proportionally we could state that the printing of 800,000 greeting cards would exceed $5 million. However, since the costs do not increase proportionally, we cannot make such specific assumptions about the costs as the number of cards printed increases. Thus, statement (1) is not sufficient to answer the question.

Statement (2): If at 600,000 cards printed we’re already exceeding costs of $6 million, it is safe to say we will exceed costs of $5 million at 700,000. Sufficient. The correct answer is (B).

# Social Distancing with Data Sufficiency Challenge! – Day 24

*And remember to take whatever precautions you need to stay healthy over the next few weeks! *

**Question #24**

4.7☆◎3

If ☆ and ◎ each represent single digits in the decimal above, what digit does ☆ represent?

(1) When the decimal is rounded to the nearest tenth, 4.8 is the result.

(2) When the decimal is rounded to the nearest hundredth, 4.77 is the result.

**Explanation**

By statement (1), we know that the hundredths digit (represented by ☆) must be equal to 5, 6, 7, 8, or 9. We cannot narrow it down further than that, so statement (1) is not sufficient.

Statement (2) shows us the hundredths digit, but it has been rounded. Since we do not know the thousandths digit, we cannot be sure whether the hundredths digit is indeed 7, or if it was rounded up from 6. Because we cannot be sure of ☆‘s value, this is not sufficient.

Even combined, we do not have enough information to answer the question. The correct answer is (E).

# Social Distancing with Data Sufficiency Challenge! – Day 23

*And remember to take whatever precautions you need to stay healthy over the next few weeks! *

**Question #23**

What distance did Marty drive?

(1) Wendy drove 15 miles in 20 minutes.

(2) Marty drove at the same average speed as Wendy.

**Explanation**

We know that statement (1) is not sufficient because it doesn’t tell us anything about Marty.

Statement (2) by itself also fails to provide enough information, since statement (2) doesn’t tell us anything about Wendy’s distance.

But it looks like it might, combined with statement (1), give us enough information to answer the question. We know how far Marty would get in any 20 minute interval, but the problem is that we don’t know how long Marty drove. The correct answer is (E).

# Social Distancing with Data Sufficiency Challenge! – Day 22

*And remember to take whatever precautions you need to stay healthy over the next few weeks! *

**Question #22**

In triangle *ABC*, if *AB* = *x*, *BC* = *x* – 1, *AC* = *y*, which of the three angles of triangle *ABC* has the smallest degree measure?

(1) *y* = *x* – 2

(2) *y* = 5

**Explanation**

In a triangle, the smallest side will be opposite the angle with the smallest degree measure. If we can identify which side is shortest, we can identify the smallest angle.

Statement (1) tells us that *AC* = y = x – 2. Since the other sides have measures of *x* and *x*-1, we know that *AC* will be the smallest side. You can test this out by making up a value for* x*. Since we know *AC* is the smallest side, we can find the angle with the smallest degree measure. Sufficient.

Statement (2) tells us the length of *y*. This does not help us determine which side is smallest, so it is not sufficient. The correct answer is (A).