Pat bought 5 pounds of apples. How many pounds of pears could he have

Pat bought 5 pounds of apples. How many pounds of pears could he have bought for same amount of money?
1) 1 pound of pears cost $0.5 more that 1 pound of apples
2) 1 pound of pears cost 1.5 times as much as 1 pound of apples

We need a relationship between price of pears and that of apples to solve the question.

STAT1
1p = 0.5 + 1a
But this relationship is not sufficient to answer because
price of 5 pounds of apples = 5p = 5*0.5 + 5a but we cannot tell for sure about the exact pounds of apples we can buy

STAT2
1p = 1.5*1a
This relationship is sufficient because
price of 5 pounds of apples = 5p = 5*1.5 *1a= 7.5a
so we know for sure that we can buy 7.5 pounds of apples with the same money.
So, Answer will be B

Hope it helps!

I didn't understand statement 2

Hello Bunuel,

Can you please correct my approach of solving this question.

Statement 1:

5 pound of apple cost x
1 pound of apple cost x/5

1 pound of pear would have cost x/5 + 0.5$. Since x is unknown . Hence not sufficient

Statement 2:

1 pound of pear cost 3/2(x/5).

Here, now i thought that since x is still unknown its not sufficient.

Combining both also doesnt give value for x. Hence my answer was E which is incorrect,

Can you please solve this question using my approach. If its correct thanks!

Hi All,

In these types of DS questions, if you're sure if a pattern exists or not, you can prove it by TESTing VALUES and being thorough. Here's how:

We're told that Pat bought 5 pounds of apples. We're asked how many pounds of pears could have been purchased with the same amount of money.

**Note: I'm going to assume that both the cost per pound of apples and the cost per pound of pears remains constant.**

Fact 1: 1 pound of pears costs $0.5 more than 1 pound of apples.

IF....
A pound of apples cost $1, then a pound of pears costs $1.50
5 pounds of apples = $5
$5 = $1.50(X pounds of pears)
X = 3 1/3 pounds of pears

IF...
A pound of applies costs $.50, then a pound of pears costs $1
5 pounds of applies = $2.50
$2.50 = $1(X pounds of pears)
X = 2.5 pounds of pears
The answer changes based on the starting price of a pound of applies.
Fact 1 is INSUFFICIENT

Fact 2: 1 pound of pears costs 1.5 times as much as 1 pound of apples

IF...
A pound of applies costs $1, then a pound of pears costs $1.50
5 pounds of applies = $5
$5 = $1.50(X pounds of pears)
X = 3 1/3 pounds of pears

A pound of applies costs $2, then a pound of pears costs $3
5 pounds of applies = $10
$10 = $3(X pounds of pears)
X = 3 1/3 pounds of pears

A pound of applies costs $0.50, then a pound of pears costs $0.75
5 pounds of apples = $2.50
$2.50 = $0.75(X pounds of pears)
X = 3 1/3 pounds of pears

In EVERY situation, we end up with the SAME number of pounds of pears.
Fact 2 is SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Hi All,

While ankurjohar's question is over 1.5 years old, I'll still answer it because that approach COULD have worked, but the work was incomplete...

Based on that user's initial steps....

$X = cost of 5 pounds of apples
$X/5 = cost of 1 pound of apples

Fact 2 tells us that 1 pound of pears costs 1.5 times the cost of 1 pound of apples.

With some Algebra, we have...

(X/5) = cost of 1 pound of apples
(3/2)(X/5) = cost of 1 pound of pears
3X/10 = cost of 1 pound of pears

At this point, ankurjohar assumed that this was insufficient, but there's still more work to do....

We now have a ratio that relates what $X will buy you in this situation:

$X buys you 5 pounds of apples

Since $(3/10)(X) buys you 1 pound of pears, $X will buy you 10/3 pounds of pears, so we CAN answer the question with this information.
Fact 2 is SUFFICIENT.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Hi

Please, is my reasoning correct?

st2: 1 pound of pears buys 1.5 pounds of apples (so to say you can change back your pears and receive apples instead). Hence 5 pounds of pears will buy 5*1.5 pounds of apples equals 7.5 pounds of apples

Hi shasadou,

Yes, the ratio that you've calculated IS correct and you can use that ratio to eventually answer the given question (although you did not do any of that work in your explanation).

GMAT assassins aren't born, they're made,
Rich

................A........P
Pounds.......5.........P
Price.........x.........y

(1) \(y=x+0,5\), \(5x=p(x+0,5)\), you cannot get rid of x, hence not sufficient
(2) \(y=1,5x\) --> \(5x=p*1,5x\) -> \(p=10/3\)

Answer B

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Pat bought 5 pounds of apples. How many pounds of pears could he have bought for same amount of money?

(1) 1 pound of pears cost $0.5 more that 1 pound of apples
(2) 1 pound of pears cost 1.5 times as much as 1 pound of apples

When you modify the original condition and the question, it is frequently given on GMAT Math, which is "2 by 2" que like the table below.

On the tables, n=? is derived from 5a=np. Generally, when one con indicates number and the other con indicates ratio, it is most likely that ratio is an answer. As for this question, in 1) number and 2) ratio, substitute p=1.5a in 2) to 5a=np and it becomes 5a=n(1.5a). Then delete a on the both equations -> 5=1.5n, n=5/1.5, which is unique and sufficient. Therefore the answer is B.


 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.

Given: Pat bought 5 pounds of apples.

Target question: How many pounds of pears could Pat have bought for the same amount of money?
This is a good candidate for rephrasing the target question.

Let A = the price per pound of apples
Let P = the price per pound of pears
If Pat bought 5 pounds of apples, then 5A = the total amount that Pat spent
Pat then wants to spend her 5A dollars on pears
So, 5A/P = the number of pounds of pears Pat can buy with the 5A dollars
REPHRASED target question: What is the value of 5A/P?

Aside: Below, you'll find a video with tips on rephrasing the target question

Statement 1: One pound of pears costs 0.50$ more than one pound of apples.
In other words, P = A + 0.5
Does this help us determine the value of 5A/P?
No.
Take 5A/P and replace P with A + 0.5 to get: 5A/P = 5A/(A + 0.5)
Since there's no way to determine the value of 5A/(A + 0.5) (aka 5A/P), we cannot answer the REPHRASED target question with certainty.
So, statement 1 is NOT SUFFICIENT

Statement 2: One pound of pears costs 3/2 times as much as one pound of apples.
In other words, P = (3/2)A or we can write P = 1.5A
Does this help us determine the value of 5A/P?
Yes!!
Take 5A/P and replace P with 1.5A to get: 5A/P = 5A/1.5A = 5/1.5 = 3 1/3
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

RELATED VIDEO

We are given that Pat bought 5 pounds of apples for some amount of money, and we are asked to determine the number of pounds of pears she could have bought for the same amount of money.

Statement One Alone:


One pound of pears costs $0.50 more than one pound of apples.

If we let a = the cost (in dollars) of a pound of apples, then a + 0.5 = the cost (in dollars) of a pound of pears. We can also let x = the number of pounds of pears that cost exactly the same as 5 pounds of apples.

Since the overall cost for 5 pounds of apples needs to be the same as for x pounds of pears, we can create the following equation:

5a = x(a + 0.5)

x = 5a/(a + 0.5)

Since we cannot determine a value for x, statement one alone is not sufficient.

Statement Two Alone:


One pound of pears costs 3/2 times as much as one pound of apples.

Once again, we can let a = the cost (in dollars) of a pound of apples. It must then be true that 1.5a = the cost (in dollars) of a pound of pears. We also can let x = the number of pounds of pears that cost exactly the same as 5 pounds of apples.

Since the overall cost for 5 pounds of apples needs to be the same as for x pounds of pears, we can create the following equation:

5a = x(1.5a)

x = 5a/(1.5a)

x = 5/1.5

x = 10/3 = 3.33 lbs

Statement two alone is sufficient.

Answer: B

TL;DR

Pounds=?

1) If 1b of apple = 1, 5/1.5 >3
If 1b of apple = 2, # = 10/2.5 = 4 NS

2) If 1b of apple = 1, 5/1.5
If 1b of apple = 2, # = 10/3 = 5/1.5 Sufficient

Veritas Prep Official Solution

Statement 1 can be tested by picking numbers. Say apples cost $1/pound. The total cost of 5 pounds of apples would be $5. If one pound of pears cost $.50 more than one pound of apples, then one pound of pears would cost $1.50. The number of pounds of pears that could be purchased for $5 would be 5/1.5 = 10/3. So that’s one possibility.

Now say apples cost $2/pound. The total cost of 5 pounds of apples would be $10. If one pound of pears cost $.50 more than one pound of apples, then one pound of pears would cost $2.50. The number of pounds of pears that could be purchased for $10 would be 10/2.5 = 4. Because we get different results, this Statement alone is not sufficient to answer the question.

Statement 2 tells us that one pound of pears costs 1 ½ times (or 3/2 times) as much as one pound of apples. Remember that reciprocal relationship! If the ratio of the price per pound for pears and the price per pound for apples is 3/2, then the ratio of their respective quantities must be 2/3. If we could buy five pounds of apples for a given cost, then we must be able to buy (2/3) * 5 = (10/3) pounds of pears for that same cost. Because we can find a single unique value, Statement 2 alone is sufficient to answer the question, and we know our answer must be B.

Pat bought 5 pounds of apples. Let the amount paid by him for the same be $A. We are to find out how many pounds of pears he can buy for $A.
To be able to do this, we need some kind of a relationship between the costs of the two types of fruits.

From statement I alone, 1 pound of pears cost $0.5 more than 1 pound of apples.
From question data, cost of 1 pound of apples = \(\frac{A }{ 5}\).

Therefore, cost of 1 pound of pears =\(\frac{ A }{ 5}\) + \(\frac{1 }{2}\) = \(\frac{(2A + 5) }{10}\).

Number of pounds of pears Pat can buy with $A = \(\frac{A }{ (2A + 5 / 10)}\) = \(\frac{10 A }{ (2A + 5)}\), which cannot be simplified further to get a value, unless we have A.

Statement I alone is insufficient. Answer options A and D can be eliminated.

From statement II alone, 1 pound of pears cost 1.5 times as much as 1 pound of apples
From question data, cost of 1 pound of apples = \(\frac{A }{ 5}\).

Therefore, cost of 1 pound of pears = \(\frac{3}{2}\) * \(\frac{A }{5}\) = \(\frac{3 A }{ 10}\).

Number of pounds of pears Pat can buy with $ A = \(\frac{A }{ (3A/10)}\) = \(\frac{10 }{ 3}\).

Another way to look at this information is – if you are multiplying the cost by 3/2, you need to multiply the quantity by 2/3 so that the expenditure remains the same. Therefore, to keep A constant, you multiply 5 with (2/3) to get (10/3) pounds.

Statement II alone is sufficient. Answer options C and E can be eliminated.

The correct answer option is B.

Hope that helps!
Aravind B T

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