# Social Distancing with Data Sufficiency Challenge! – Day 20

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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 #20

If x – y = z, what is the value of y?

(1) x = 7

(2) z = x + 4

Explanation

Statement (1) is insufficient because, if we plug in x = 7 we are left with: 7 – y = z … and we still are unable to solve for y‘s value.

Let’s try plugging in statement (2): x – y = z … x – y = (x + 4) … -y = 4 … y = -4:  Statement (2) alone is sufficient! The correct answer is (B).

# Social Distancing with Data Sufficiency Challenge! – Day 19

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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 #19

If j and k are integers, is j + k an odd integer?

(1) j > 12

(2) j = k – 1

Explanation

This is a pretty straightforward number properties question drilling us on our odds and evens rules. Remember that when adding, the only way to end up with an odd sum is to have an odd number of odd values in the list of numbers to be added together. If this is unclear, pick a few different values– odds and evens– and test it out! 🙂

Statement (1) doesn’t give us much to work with. It’s certainly not sufficient.
Statement (2) is enough to know for certain that the sum of j and k would be odd. Make up a few numbers to check it out. You’ll find that the sum of consecutive integers is always odd. Sufficient. The correct answer is (B).

# Social Distancing with Data Sufficiency Challenge! – Day 18

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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 #18

Is the number x between .5 and .9 ?

(1) 800x < 620

(2) 1200x > 620

Explanation

Let’s solve for x in each inequality statement.

Statement (1): 800x < 620 … x < .775  … That alone is not sufficient to say that x is in the presented range, since we can’t be sure x isn’t less than .5
Note: The easier way to think about this without using a calculator is to think about fractions and decimals you know well. Reduce this fraction first by ten (80x < 62), then cut it in half (40x < 31), and finally isolate the x: x < 31/40.  What’s really close to 31/40 that you know well? Let’s use 3/4, which equals .75.

Statement (2) = 1200x > 620 … x > .517 … Statement (2) is also not sufficient alone.
Suggestion: Handle this calculation the same way as you did statement (1). 1200x > 620 … reduce by ten: 120x > 62 … cut in half: 60x > 31 … isolate x: x > 31/60 which is just barely more than .5 … no lengthy calculation needed!

But combined with statement (1), we know that x is in the range: .517 < x < .775, which is within the range presented of .5 < x < .9

# Social Distancing with Data Sufficiency Challenge! – Day 17

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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 #17

Is x a positive number?

(1) 8x > 7x

(2) x – 2 is negative.

Explanation

Statement (1) is sufficient, since that inequality would only hold true for a positive value of x. Make up some numbers to test it out. We know statement (2) is not sufficient because there are both positive and negative values of x that satisfy the statement “x – 2 is negative.” The correct answer is (A).

# Social Distancing with Data Sufficiency Challenge! – Day 16

Photo by Pixabay on Pexels.com

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 #16

Milk flows into a vat at a constant rate through a metal pipe. At the same time, milk is pumped out of the vat at a constant rate through another metal pipe. At what rate, in liters per minute, is the amount of milk in the vat decreasing?

(1) The amount of milk initially in the vat was 100 liters.

(2) Milk flows into the vat at a rate of 5 gallons every 5 minutes and out of the vat at a rate of 5 gallons per minute.

Explanation

The amount of milk initially in the vat is irrelevant, since we’re only interested in the rate of milk decrease, so statement (1) is not sufficient. Statement (2) tells us separate rates for the milk flowing into and out of the vat. Using these rates, we can find an overall rate for the decrease of milk volume.

Don’t bother finding the actual rate! To answer this question, you just need to confirm that it is possible to calculate — don’t waste time actually doing the math. Statement (2) alone is sufficient. The correct answer is (B).

# Social Distancing with Data Sufficiency Challenge! – Day 15

Photo by Jeswin Thomas on Pexels.com

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 #15

Is 3 < x < 4 ?

(1) 1 < x

(2) x < 5

Explanation

Statement (1):  Some values greater than 1 are between 3 and 4, but not all are.  X could be, say, 3.5 or 7.  INSUFFICIENT.  We can eliminate answers A and D.

Statement (2):  Some values less than 5 are between 3 and 4, but not all are.  INSUFFICIENT.  Eliminate answer B.

Even taken together the two statements don’t  yield a definite answer, either “yes” or “no.”  Combined, they give a range for x of: 1 < x < 5.   X could be 2 (no) or 4 (yes). The correct answer is (E).

# Social Distancing with Data Sufficiency Challenge! – Day 14

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 #14

If n is an integer, is n – 1 even?

(1) n – 2 is odd

(2) n + 1 is even

Explanation

If n – 2 is odd, then we know that n itself must be odd. Not sure about that? Make up some numbers and test it out. So if n is odd, then n – 1 must be even. Statement (1) is sufficient.
Statement (2) tells us that n + 1 is even. That means that n is odd, which means that n – 1 is also even. Statement (2) is also sufficient! The correct answer is (D).

# Social Distancing with Data Sufficiency Challenge! – Day 13

Photo by Louis Bauer on Pexels.com

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 #13

Is x greater than 2.7 ?

(1) x > 2.6

(2) x > 2.8

Explanation

If x > 2.6, we still can’t be sure it is greater than 2.7. It could be 2.65, or 2.8…so statement (1) is not sufficient.

Statement (2), on the other hand, is sufficient. If x > 2.8, then we know with certainty that it is greater than 2.7. The correct answer is (B).

# Social Distancing with Data Sufficiency Challenge! – Day 12

Photo by Juhasz Imre on Pexels.com

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 #12

Is the integer m a prime number?

(1) 2m = 10

(2) 3 < m < 6

Explanation

A number is prime when it has exactly two factors: itself and 1 (NB: 1 is not a prime number because it only has one factor, itself which is one).

With statement (1), we can solve for a single value of m (and that’s enough to know we can get an absolute yes or absolute no, so you can mark this one as sufficient here and move on to the next statement). If you want to see it: 2m = 10; m = 5; 5 is prime: Sufficient.

Statement (2) gives us a range of integers that includes 4 and 5. Since 5 is prime and 4 is not prime, this statement is NOT sufficient to answer the question. The correct answer is (A).

# Social Distancing with Data Sufficiency Challenge! – Day 11

Photo by Pixabay on Pexels.com

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 #11

A rope has four knots labeled A, B, C, and D, in that order. What is the rope distance between knots B and C?

(1) The rope distance between knots A and C is 5 feet.

(2) The rope distance between knots B and D is 7 feet.

Explanation

Neither of the statements alone is sufficient. It may be tempting to think that together the statements can answer the question — by subtracting the two distances. Even combined, however, the information is insufficient.

We have no information about the distances between A and B or between C and D. If you’re having a tough time understanding this one, try drawing a couple examples where the distance of BC varies even when AC is 5 and BD is 7 to prove it. The correct answer is (E).