At a certain picnic, each of the guests was served either a single scoops or a double scoop of ice cream. How many of the guests were served a double scoop of ice cream?
1. at the picnic, 60% of the guests were served a double scoop of ice cream.
2. a total of 120 scoops of ice cream were served to all the guests at the picnic.
Could you pls show me the number of the guests who were served a double scoop?
Thanks.
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scoops of ice cream - DS 55 from OG 11
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Stuart@KaplanGMAT
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We have 2 variables (D and S) and no equations. We want to solve for D. We need either 2 more equations or 1 equation with just D in it.maria wrote:At a certain picnic, each of the guests was served either a single scoops or a double scoop of ice cream. How many of the guests were served a double scoop of ice cream?
1. at the picnic, 60% of the guests were served a double scoop of ice cream.
2. a total of 120 scoops of ice cream were served to all the guests at the picnic.
Could you pls show me the number of the guests who were served a double scoop?
Thanks.
(1) gives us one equation with D & S - insufficient.
(2) gives us one equation with D & S - insufficient.
Together, we have two distinct linear equations and two unknowns: sufficient.
The concept of # of equations and # of unknowns is THE most powerful weapon in your data sufficient arsenal. Learn the rule. Love the rule. Be the rule!
If for some reason we wanted to actually solve (remember, in DS we don't care what the answer actually is), here's a translation of the equations:
(1) We know the ratio of d/s = 3/2 (60%/40%)
(2) Well, a double scoop has two scoops and a single scoop has 1 scoop. So:
2D + S = 120
From (1) (after some rearranging):
S = (2/3)D
Substituting into (2):
2D + (2/3)D = 120
(6/3)D + (2/3)D = 120
(8/3)D = 120
D = (3/8)120 = 3*15 = 45
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Vemuri
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I have come across this question more than a couple of times (in an interval of few weeks, so my memory kind of gets reset & does not remember the answer choices when I attempt again) & everytime I try to solve it, I chose my answer as B. Its amazing how I do it so consistently. I think the root cause to the problem is my agreement with the explanation provided in OG.Stuart Kovinsky wrote: (2) Well, a double scoop has two scoops and a single scoop has 1 scoop. So:
2D + S = 120
According to me if a Single scoop is considered as 'x', then a double scoop is '2x'. So, based on statement 2, if a total of 120 scoops were served to all the guests (and the question states that each of the guests was served either a single scoop or a double scoop), my equation is:
x+2x =120 ==> 3x=120 ==> x=40 (single scoops). So, double scoops served are '80'.
Where am I going wrong? Appreciate your responses.
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Vemuri
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And it is also amazing how I mostly answer my own doubts when posting on www.beatthegmat.comVemuri wrote:I have come across this question more than a couple of times (in an interval of few weeks, so my memory kind of gets reset & does not remember the answer choices when I attempt again) & everytime I try to solve it, I chose my answer as B. Its amazing how I do it so consistently. I think the root cause to the problem is my agreement with the explanation provided in OG.Stuart Kovinsky wrote: (2) Well, a double scoop has two scoops and a single scoop has 1 scoop. So:
2D + S = 120
According to me if a Single scoop is considered as 'x', then a double scoop is '2x'. So, based on statement 2, if a total of 120 scoops were served to all the guests (and the question states that each of the guests was served either a single scoop or a double scoop), my equation is:
x+2x =120 ==> 3x=120 ==> x=40 (single scoops). So, double scoops served are '80'.
Where am I going wrong? Appreciate your responses.
. I just realised after posting that I need to know the ratio of Single scoops & Double scoops being served. The equation I set above is incorrect because I am only considering the # of scoops & not differentiating Double scoops & Single scoops.I have a similar problem that I can't seem to make out correctly. Does anyone have any suggestions?
Steve took a math test that consists of basic questions and advanced questions. A correct answer to the basic question will gain 1 point and a correct answer to advanced question will gain 2 points. How many questions does the test consist of?
(1) Steve answered 80% of the basic question and 30% of the advanced questions correctly, and gained 88 points.
(2) There are twice as many advanced questions as the basic question.
My thinking was B = basic Questions, A = Advanced questions
(0.8)B+0.3(A) = 88
A/B = 2/1, then A = 2B; then substitution:
0.8(B) + 0.3(2B)=88
B = 62.8 which does not see like the correct answer at all? The OG is C (which I understand, I just want to make the math work).
Steve took a math test that consists of basic questions and advanced questions. A correct answer to the basic question will gain 1 point and a correct answer to advanced question will gain 2 points. How many questions does the test consist of?
(1) Steve answered 80% of the basic question and 30% of the advanced questions correctly, and gained 88 points.
(2) There are twice as many advanced questions as the basic question.
My thinking was B = basic Questions, A = Advanced questions
(0.8)B+0.3(A) = 88
A/B = 2/1, then A = 2B; then substitution:
0.8(B) + 0.3(2B)=88
B = 62.8 which does not see like the correct answer at all? The OG is C (which I understand, I just want to make the math work).
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goyalsau
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Buddy i able to do the question, but with some slight changes.Cedagmat wrote:I have a similar problem that I can't seem to make out correctly. Does anyone have any suggestions?
Steve took a math test that consists of basic questions and advanced questions. A correct answer to the basic question will gain 1 point and a correct answer to advanced question will gain 2 points. How many questions does the test consist of?
(1) Steve answered 80% of the basic question and 30% of the advanced questions correctly, and gained 88 points.
(2) There are twice as many advanced questions as the basic question.
My thinking was B = basic Questions, A = Advanced questions
(0.8)B+0.3(A) = 88
A/B = 2/1, then A = 2B; then substitution:
0.8(B) + 0.3(2B)=88
B = 62.8 which does not see like the correct answer at all? The OG is C (which I understand, I just want to make the math work).
There are twice as many advanced questions as the basic question. { Just change it There are twice as many Basic questions as the Advance question. }
Lets assume there were 40 basic question. then there must be 20 Advanced questions.
Total marks will be 40 * 1 + 20 * 2 = 80
Now we know that 80% basic question are correct, it means 32 marks are scored from basic questions.
and we also know 30% advanced questions are correct , it means 6 questions are correct and in total 12 marks are scored of them,
in total 44 marks are scored of 80, means 55% of total marks,
Now i know 88 is 55% of total marks, it means total marks are 160,
80 questions of basic and 40 questions of Advanced.
out of 80 -- 64 are correct means 64 points
out of 40 -- 12 are correct means 24 points.
in total 88 points.
I changed the questions. Because i was not getting the answer. From the previous question.
and please if you have the official explanation. Do share......... it ....
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I just did this question few minutes ago, I choosed E because I thought "either...or" doesn't mean the guests should choose only one and not more. I remember in other questions, it is explicitely mentionned that X has to choose A or B but only one.Stuart Kovinsky wrote:We have 2 variables (D and S) and no equations. We want to solve for D. We need either 2 more equations or 1 equation with just D in it.maria wrote:At a certain picnic, each of the guests was served either a single scoops or a double scoop of ice cream. How many of the guests were served a double scoop of ice cream?
1. at the picnic, 60% of the guests were served a double scoop of ice cream.
2. a total of 120 scoops of ice cream were served to all the guests at the picnic.
Could you pls show me the number of the guests who were served a double scoop?
Thanks.
(1) gives us one equation with D & S - insufficient.
(2) gives us one equation with D & S - insufficient.
Together, we have two distinct linear equations and two unknowns: sufficient.
The concept of # of equations and # of unknowns is THE most powerful weapon in your data sufficient arsenal. Learn the rule. Love the rule. Be the rule!
If for some reason we wanted to actually solve (remember, in DS we don't care what the answer actually is), here's a translation of the equations:
(1) We know the ratio of d/s = 3/2 (60%/40%)
(2) Well, a double scoop has two scoops and a single scoop has 1 scoop. So:
2D + S = 120
From (1) (after some rearranging):
S = (2/3)D
Substituting into (2):
2D + (2/3)D = 120
(6/3)D + (2/3)D = 120
(8/3)D = 120
D = (3/8)120 = 3*15 = 45
So my question is : is "either...or" sufficient to conclude that people (for example) have to choose only once and not more?
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bbq11223344
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Stuart Kovinsky wrote:We have 2 variables (D and S) and no equations. We want to solve for D. We need either 2 more equations or 1 equation with just D in it.maria wrote:At a certain picnic, each of the guests was served either a single scoops or a double scoop of ice cream. How many of the guests were served a double scoop of ice cream?
1. at the picnic, 60% of the guests were served a double scoop of ice cream.
2. a total of 120 scoops of ice cream were served to all the guests at the picnic.
Could you pls show me the number of the guests who were served a double scoop?
Thanks.
(1) gives us one equation with D & S - insufficient.
(2) gives us one equation with D & S - insufficient.
Together, we have two distinct linear equations and two unknowns: sufficient.
The concept of # of equations and # of unknowns is THE most powerful weapon in your data sufficient arsenal. Learn the rule. Love the rule. Be the rule!
If for some reason we wanted to actually solve (remember, in DS we don't care what the answer actually is), here's a translation of the equations:
(1) We know the ratio of d/s = 3/2 (60%/40%)
(2) Well, a double scoop has two scoops and a single scoop has 1 scoop. So:
2D + S = 120
From (1) (after some rearranging):
S = (2/3)D
Substituting into (2):
2D + (2/3)D = 120
(6/3)D + (2/3)D = 120
(8/3)D = 120
D = (3/8)120 = 3*15 = 45
hi you did solve the problem.but I have a question in mind:
you put d/s = 3/2,but capital 2D + S = 120.the "d" is actually not the same thing as D,right?
so the "2D + S = 120" should be modified as D + S = 120.
=> D = 72 , S = 48
ok.let me know if I were wrong~lol
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viveksahay
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Couldn't agree morebbq11223344 wrote:Stuart Kovinsky wrote:We have 2 variables (D and S) and no equations. We want to solve for D. We need either 2 more equations or 1 equation with just D in it.maria wrote:At a certain picnic, each of the guests was served either a single scoops or a double scoop of ice cream. How many of the guests were served a double scoop of ice cream?
1. at the picnic, 60% of the guests were served a double scoop of ice cream.
2. a total of 120 scoops of ice cream were served to all the guests at the picnic.
Could you pls show me the number of the guests who were served a double scoop?
Thanks.
(1) gives us one equation with D & S - insufficient.
(2) gives us one equation with D & S - insufficient.
Together, we have two distinct linear equations and two unknowns: sufficient.
The concept of # of equations and # of unknowns is THE most powerful weapon in your data sufficient arsenal. Learn the rule. Love the rule. Be the rule!
If for some reason we wanted to actually solve (remember, in DS we don't care what the answer actually is), here's a translation of the equations:
(1) We know the ratio of d/s = 3/2 (60%/40%)
(2) Well, a double scoop has two scoops and a single scoop has 1 scoop. So:
2D + S = 120
From (1) (after some rearranging):
S = (2/3)D
Substituting into (2):
2D + (2/3)D = 120
(6/3)D + (2/3)D = 120
(8/3)D = 120
D = (3/8)120 = 3*15 = 45
hi you did solve the problem.but I have a question in mind:
you put d/s = 3/2,but capital 2D + S = 120.the "d" is actually not the same thing as D,right?
so the "2D + S = 120" should be modified as D + S = 120.
=> D = 72 , S = 48
ok.let me know if I were wrong~lol
I was really eager to post a reply after seeing the expression 2D + S = 120 but was a bit hesitant. But as I read the post further I realized atleast one more person has the same doubt
But I think she is correct because another post on urch has also the same solution : https://www.urch.com/forums/gmat-data-su ... cream.html
But I still dont get the expression 2D + S = 120
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Hi viveksahay & bbq11223344!viveksahay wrote:Couldn't agree morebbq11223344 wrote:hi you did solve the problem.but I have a question in mind:
you put d/s = 3/2,but capital 2D + S = 120.the "d" is actually not the same thing as D,right?
so the "2D + S = 120" should be modified as D + S = 120.
=> D = 72 , S = 48
ok.let me know if I were wrong~lol
I was really eager to post a reply after seeing the expression 2D + S = 120 but was a bit hesitant. But as I read the post further I realized atleast one more person has the same doubt
But I think she is correct because another post on urch has also the same solution : https://www.urch.com/forums/gmat-data-su ... cream.html
But I still dont get the expression 2D + S = 120
Let's just write these equations out again and be a bit more explicit about what every variable is doing to clear up the confusion (cause I can definitely see how this gets confusing FAST)!
The Stem: "At a certain picnic, each of the guests was served either a single scoops or a double scoop of ice cream. How many of the guests were served a double scoop of ice cream?"
If each guest (meaning every) was served either 1 or 2, then those are the only options. But we don't know how many of either so let's start organizing our info!
SINGLE SCOOP:
S = # of guests getting Singles
1 = # of scoops per serving
...so the total scoops served from Single would be S*1 = S
DOUBLE SCOOP:
D = # of guests getting doubles
2 = # of scoops per serving
...so the total scoops served from Double would be D*2 = 2D
...and total guests would = (S + D)
What we need to find? D
Statement (1): "at the picnic, 60% of the guests were served a double scoop of ice cream. "
If the total # of guests is (S+D), then .6(S+D) = D
.6S + .6D = D
.6S = .4D
6S = 4D
3S = 2D
but can't solve for D!
Statement (2): "a total of 120 scoops of ice cream were served to all the guests at the picnic."
okay, this is asking about total scoops, so we get S total scoops from the single servings, and 2D total scoops from the double servings, so...
S + 2D = 120
2D = 120 - s
D = 60 - .5S
Can't solve for D
Statement (1+2): Putting them together
3S = 2D
S + 2D = 120
Plug in for 2D...
S + 3S = 120
4S = 120
S = 30
3S = 2D
3(30) = 2D
90 = 2D
D = 45
Hope this helps!
Whit
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Hi goyalsau & Cedagmat!goyalsau wrote:Buddy i able to do the question, but with some slight changes.Cedagmat wrote:I have a similar problem that I can't seem to make out correctly. Does anyone have any suggestions?
Steve took a math test that consists of basic questions and advanced questions. A correct answer to the basic question will gain 1 point and a correct answer to advanced question will gain 2 points. How many questions does the test consist of?
(1) Steve answered 80% of the basic question and 30% of the advanced questions correctly, and gained 88 points.
(2) There are twice as many advanced questions as the basic question.
My thinking was B = basic Questions, A = Advanced questions
(0.8)B+0.3(A) = 88
A/B = 2/1, then A = 2B; then substitution:
0.8(B) + 0.3(2B)=88
B = 62.8 which does not see like the correct answer at all? The OG is C (which I understand, I just want to make the math work).
There are twice as many advanced questions as the basic question. { Just change it There are twice as many Basic questions as the Advance question. }
Lets assume there were 40 basic question. then there must be 20 Advanced questions.
Total marks will be 40 * 1 + 20 * 2 = 80
Now we know that 80% basic question are correct, it means 32 marks are scored from basic questions.
and we also know 30% advanced questions are correct , it means 6 questions are correct and in total 12 marks are scored of them,
in total 44 marks are scored of 80, means 55% of total marks,
Now i know 88 is 55% of total marks, it means total marks are 160,
80 questions of basic and 40 questions of Advanced.
out of 80 -- 64 are correct means 64 points
out of 40 -- 12 are correct means 24 points.
in total 88 points.
I changed the questions. Because i was not getting the answer. From the previous question.
and please if you have the official explanation. Do share......... it ....
Very interesting question, and goyalsau, I like that you were able to solve the answer by craftily picking numbers that happened to give the correct 88 points! But how would we solve this problem algebraically from the start (both the original and the edited version). Well, I'm going to do both, because Cedagmat is right that the math doesn't quite come out with the original but not in the way you initially said (I'll point out the calculation error you made as we go). But you end up with the student getting a fractional number of questions right (35.2 of the basic and 26.4 of the advanced, and that doesn't make sense - but just so you can check your math I'll run through it!)
ORIGINAL QUESTION
Stem:"Steve took a math test that consists of basic questions and advanced questions. A correct answer to the basic question will gain 1 point and a correct answer to advanced question will gain 2 points. How many questions does the test consist of?"
Let's organize our information:
A = # of Advanced questions on the test
2 = value of each CORRECT Advanced question
B = # of Basic questions on the test
1 = value of each CORRECT Basic question
A+B = Total # of questions on the test
What are we looking for? A+B
Statement (1):"Steve answered 80% of the basic question and 30% of the advanced questions correctly, and gained 88 points."
If he answered 80% of the Basic questions correctly, then he answered .8(B). For each of those, he scored only 1 point. So 1 point each would be .8(B)(1).
If he answered 30% of the Advanced questions correctly, then he answered .3(A). For each of those, he scored 2 points. So 2 point each would be .3(A)(2). [/i](notice that this is where you made your mathematical mistake Cedagmat - you forgot to count each correct Advanced as 2 points).[/i]
Adding these up, we should get the total of 88 points...
.8B + .3A(2) = 88
.8B + .6A = 88
(simplify)
8B + 6A = 880
4B + 3A = 440
But I can't get the sum of A + B, so [spoiler]NOT SUFFICIENT![/spoiler]
Statement (2):"There are twice as many advanced questions as there are basic questions."
The easiest way to set these up is the ratio:
A/B = 2/1
A = 2B
I can rewrite this as A-2B, but I can't get the SUM of A+B, so [spoiler]NOT SUFFICIENT![/spoiler]
Statement (1+2):Putting it together
4B + 3A = 440 ...AND... A = 2B
4B + 3(2B) = 440
10B = 440
B = 44
A = 2(44) = 88.
A+B = 88+44 = 132
SUFFICIENT
**BUT - here is the problem...remember that Steve got 80% of the Basic problems and 30% of the Advanced problems correct. That would be .8(44)=35.2 and .3(88)=26.4, and even though you never needed to solve for these specific values, the test wouldn't write a question that would have these exist. SO, lets use goyalsau's edits and just rework starting with Statement 2.
EDITED VERSION
Statement (2):"There are twice as many BASIC questions as there are ADVANCED questions."
The easiest way to set these up is the ratio:
B/A = 2/1
B = 2A
I can rewrite this as -2A+B, but I can't get the SUM of A+B, so [spoiler]NOT SUFFICIENT![/spoiler]
Statement (1+2):Putting it together
4B + 3A = 440 ...AND... B = 2A
4(2A) + 3A = 440
8A + 3A = 440
11A = 440
A = 40
B = 2(40) = 80.
A + B = 120
SUFFICIENT
**Now lets check the issue from the last version. Steve got 80% of the Basic problems and 30% of the Advanced problems correct. That would be .8(80)=64 and .3(40)=12. These are whole numbers and make logical sense so this is likely the way the actual test would present this question!
NICE Example you guys!! What great practice!
Hope this explanation helped!
Whit
Whitney Garner
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I tried to do it as below...
As both statements are individually insufficient so 1+2
D/S = 3/2 or 3x/2x
Total no. of scoops is 120 so 3x+2x = 120
x = 24
No. of double scoops = 3*24 = 72
no. of single scoops = 2*24 = 48
As the answer coming is different from the answers of others...I am sure I am doing something wrong somewhere but cant figure out....Can anyone please point out where I am going wrong...Many thanks in advance...
As both statements are individually insufficient so 1+2
D/S = 3/2 or 3x/2x
Total no. of scoops is 120 so 3x+2x = 120
x = 24
No. of double scoops = 3*24 = 72
no. of single scoops = 2*24 = 48
As the answer coming is different from the answers of others...I am sure I am doing something wrong somewhere but cant figure out....Can anyone please point out where I am going wrong...Many thanks in advance...
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GMATGuruNY
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The portion in red doesn't divide the scoops accurately.bharti06 wrote:I tried to do it as below...
As both statements are individually insufficient so 1+2
D/S = 3/2 or 3x/2x
Total no. of scoops is 120 so 3x+2x = 120
x = 24
No. of double scoops = 3*24 = 72
no. of single scoops = 2*24 = 48
As the answer coming is different from the answers of others...I am sure I am doing something wrong somewhere but cant figure out....Can anyone please point out where I am going wrong...Many thanks in advance...
Since each double-scoop guest receives TWO SCOOPS, the equation should be:
2(3x) + 2x = 120
8x = 120
x = 15.
Thus, the number of double-scoop guests = 3x = 3*15 = 45.
I posted a solution here:
https://www.beatthegmat.com/picnic-icecr ... 16693.html
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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GMATGuruNY wrote:The portion in red doesn't divide the scoops accurately.bharti06 wrote:I tried to do it as below...
As both statements are individually insufficient so 1+2
D/S = 3/2 or 3x/2x
Total no. of scoops is 120 so 3x+2x = 120
x = 24
No. of double scoops = 3*24 = 72
no. of single scoops = 2*24 = 48
As the answer coming is different from the answers of others...I am sure I am doing something wrong somewhere but cant figure out....Can anyone please point out where I am going wrong...Many thanks in advance...
Since each double-scoop guest receives TWO SCOOPS, the equation should be:
2(3x) + 2x = 120
8x = 120
x = 15.
Thus, the number of double-scoop guests = 3x = 3*15 = 45.
I posted a solution here:
https://www.beatthegmat.com/picnic-icecr ... 16693.html
Oh yes...I understood it now...Thanks a ton, Mitch!!!
