At a restaurant, five friends each purchased a sandwich. Did the sum

Question

Competition Mode Question

At a restaurant, five friends each purchased a sandwich. Did the sum of the five sandwiches exceed $70?

(1) The price of the least expensive sandwich exceeded $13.

(2) The price of the most expensive sandwich exceeded $18.

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Leadership · Answer

At a restaurant, five friends each purchased a sandwich. Did the sum of the five sandwiches exceed $70?

(1) The price of the least expensive sandwich exceeded $13.
 We can assume the least expensive sandwich cost - $13.1 and others as $13.2, $13.3, $13.4 and $13.5 - Their sum does not exceed $70
whereas in another situation we take the same least expensive sandwich cost - $13.1 and others as $15, $15, $15 and $15 - Their sum exceed $70
Two different possibilities. Insufficient.

A D  / B C E

(2) The price of the most expensive sandwich exceeded $18.
 We can assume the most expensive sandwich cost - $18.1 and others as $17.9, $17.8, $17.7 and $17.6 - Their sum exceed $70
whereas in another situation we take the same most expensive sandwich cost - $18.1 and others as $10, $10, $10 and $10 - Their sum does not exceeds $70
Two different possibilities. Insufficient.

A D  /  B  C E

Combining both situations, we can assume min. cost as $13.1 and max. cost as $18.1. The three other costs will lie in between these costs. Hence, we can take $13.1 or $13.2 each for the other three - $18.1 + $13.1 + $13.1 + $13.1 + $13.1 = it exceed $70 always. Sufficient.

'C' is the winner.

freedom128 · Answer

Q. Did the price sum of the 5 sandwiches > $70?

(1) The price of the least expensive sandwich exceeded $13.
If the price of 5 sandwiches is $13.1, $13.1, $13.1, $13.1, and $13.1, respectively, then the price sum is $65.5 < $70.
If the price of 5 sandwiches is $13.1, $13.1, $13.1, $13.1, and $18.1, respectively, then the price sum is $70.5 > $70.
NOT SUFFICIENT

(2) The price of the most expensive sandwich exceeded $18.
If the price of 5 sandwiches is $10.1, $10.1, $10.1, $10.1, and $18.1, respectively, then the price sum is $58.5 < $70.
If the price of 5 sandwiches is $13.1, $13.1, $13.1, $13.1, and $18.1, respectively, then the price sum is $70.5 > $70.
NOT SUFFICIENT

1)+2)
If the price of 5 sandwiches is $13.1, $13.1, $13.1, $13.1, and $18.1, respectively, then the price sum is $70.5 > $70.
Any other possible scenarios will yield a price sum > $70.
SUFFICIENT

FINAL ANSWER IS (C)

Jawad001 · Answer

From statement (1), Least Expensive sandwich exceeded $13.

There is no mention of specific price of five sandwiches. So we cannot say the sum of five sandwiches.
From statement (2), There is no mention of specific price of any sandwiches. So we cannot say the sum of five sandwiches .

From stmnt (1) and (2) , We cannot say the sum of five sandwiches.(E)

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QuantMadeEasy · Answer

(1) The price of the least expensive sandwich exceeded $13.
price of sandwiches can be 13.1+13.2+13.2+13.2+13.2 = 65.5
Or it can be 14+15+15+15+15 = 74
Insufficient

(2) The price of the most expensive sandwich exceeded $18.
Same reasoning as above. Insufficient

(1)+(2); minimum price can be 13.1+13.2+13.2+13.2+18.1 = 70.8
Sufficient

C is correct

CareerGeek · Answer

At a restaurant, five friends each purchased a sandwich. Did the sum of the five sandwiches exceed $70?

(1) The price of the least expensive sandwich exceeded $13.
--> Price of 5 sandwiches always exceeds 5*13 = 65
--> Price > 65 
--> Price can be less than $70 or greater than $70 -->  Insufficient

(2) The price of the most expensive sandwich exceeded $18.
Case 1: Possible values of 5 sandwich prices = {19, 18, 18, 18, 18}, Sum = 91 > $70
Case 2: Possible values of 5 sandwich prices = {19, 1, 1, 1, 1}, Sum = 23 < $70
-->  Insufficient

Combining (1) & (2),
Least prize is > $13 & highest prize > $18
--> Least sum is always greater than 13 + 13 + 13 + 13 + 18 
--> Least sum > $70 ALWAYS -->  Sufficient

Option C

Archit3110 · Answer

determine whether a+b+c+d+e >$70
#1The price of the least expensive sandwich exceeded $13.
so if least expensive 13.1 $ ; others can be 14$ we get no
and if least expensive is 13.1$ ; and others can be >=15 we get yes
insufficient
#2
The price of the most expensive sandwich exceeded $18.
least expensive can be 1$ ; NO
other can be 17.9$ we get Yes
insufficient
from 1 &2
it has to be yes ; as least 13.1 and expensive ; 18.1
price of 3 other ; 13.1<price<18.1
sufficient
IMO C

At a restaurant, five friends each purchased a sandwich. Did the sum of the five sandwiches exceed $70?

(1) The price of the least expensive sandwich exceeded $13.

(2) The price of the most expensive sandwich exceeded $18.

Staphyk · Answer

At a restaurant, five friends each purchased a sandwich. Did the sum of the five sandwiches exceed $70?

Let the cost of the sandwich =
$a ,$b,$c,$d,$e
Question is $a+$b+$c+$d+$e > 70? Yes or No $a+$b+$c+$d+$e <= 70 ?

(1) The price of the least expensive sandwich exceeded $13.
assuming :a<b<c<d<e
Then we have a= 13.01 ,b=13.02,c=13.03,d=13.04,e=13.05
(13.01+13.02+13.03+13.04+13.05)=65.15
So Nope! Sum of the five sandwiches dos not exceed $70.00

Again ,a=15,b=18,c=22,d=25,e=30
Sum =$110
So here yep! Sum of the five sandwiches exceed $70
.: Not Sufficient

(2) The price of the most expensive sandwich exceeded $18.
Assuming: a<b<c<d<e
Let e= 18.01
So d=18.00,c=17.01,b=17.00,a=16.01
So yep! Sum = 86.03 >70.00

Again, let e=18.01
So d= 4,c=3,b=2,a=1
Here Nope! Sum =28.01<70.00
Not sufficient

(1+2) let least price =13.01, expensive =18.01
Now we can this 5 Dudes purchase price as follows:
13.01,13.01,13.01,13.01,18.01
Yep! Sum =70.05 >70.00
Or
Least price =13.0001, expensive =18.0001
13.0001....4 of them and an 18.0001
Yep! Sum =70.0005>70.00
Or
Least price =14 ,expensive =18
Dudes purchase price as follows
14,15,16,17,18
Sum =80>70. (Sufficient)

Hit that C

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unraveled · Answer

At a restaurant, five friends each purchased a sandwich. Did the sum of the five sandwiches exceed $70?

Let the price of five sandwiches be a, b, c, d and e.
So Is a + b + c + d + e > 70?

(1) The price of the least expensive sandwich exceeded $13.
Case I: 
Least sum of all sandwiches > 13 * 5 > 65 NO

Case II: 
13 + 13 + 13 + 13 + 20 > 72 YES

INSUFFICIENT.

(2) The price of the most expensive sandwich exceeded $18.
Case I: 
10 + 10 + 10 + 10 + 19 = 59 NO

Case II:
15 + 15 + 15 + 15 + 18.1 = 78.1 YES

INSUFFICIENT.

Together 1 and 2
13 + 13 + 13 + 13 + 18.1 = 70.1 YES (an atleast-sum case)

SUFFICIENT.

Answer C.

eakabuah · Answer

We know five friends each purchased a sandwich at a restaurant. We are to determine if the sum of the cost of the five sandwiches exceed $70.

Statement 1: The price of the least expensive sandwich exceeded $13.
From statement 1, we know that the minimum cost of a sandwich is more than $13. So lets say its $14. Lets assume that all five friends went for the least expensive sandwich that we are assuming is $14. Total cost = 14*5 = $70. The answer is No.
What about if they all opt for a $15 sandwich each. the total cost = 15*5 = $75. The answer is Yes.
Statement 1 is insufficient.

Statement 2: The price of the most expensive sandwich exceeded $18.
Lets assume that all five friends opt the most expensive sandwich and that the cost of the most expensive sandwich is $19. Then the total cost = 19*5 = $95. The answer is Yes.
How about if they all opt for a sandwich that costs $14. The total cost will now be 14*5 = $70. The answer is No.
Statement 2 is therefore insufficient.

1+2
Still insufficient since no new information is available to determine the specific orders placed by the five friends. We can therefore speculate about the cost of a sandwich and arrive at Yes and No answers to the question posed.

The answer is E.

lacktutor · Answer

At a restaurant, five friends each purchased a sandwich. Did the sum of the five sandwiches exceed $70?

(Statement1): ) The price of the least expensive sandwich exceeded $13.

let’s say that the price of each of other 4 sandwiches is $ 14.
—> 13+ 14*4= 13+ 56= $ 69.(No)

if the price of each of other 4 sandwiches is $15, then 
—> 13+ 15*4= 73(Yes) 
Insufficient

(Statement2): The price of the most expensive sandwich exceeded $18.

If the price of each of other 4 sandwiches is $12, then 
—> 12*4+ 18= 60 (No)

If the price of each of other 4 sandwiches is $15, then 
—> 15*4+ 18= 78 (Yes) 
Insufficient

Taken together 1&2, 
Sandwich(least expensive) = $13
Sandwich(most expensive) = $18

let’s say that the price of each of other 3 sandwiches is at least $13, 
—> 13+ 13*3+ 18 = 70
The price of each of other 3 sandwiches is between $13(not inclusive) and $18(not inclusive)
—> the price of 5 sandwiches is always greater than $70. 
Sufficient

The answer is C

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joohwangie · Answer

At a restaurant, five friends each purchased a sandwich. Did the sum of the five sandwiches exceed $70?

(1) The price of the least expensive sandwich exceeded $13.

13(5)=65
Total price of the sandwich > 65
Can be 65.1, 66, or more than 70
insufficient

(2) The price of the most expensive sandwich exceeded $18.

Don’t know the least expensive sandwich it can be $19x1 + $1x4 
Or the most expensive can be $100 and it’s over $70 already
Insufficient

Together
13(4)+18(1)=70
At least 13 and at least 18
Therefore together >70
Sufficient
C

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debjit1990 · Answer

Ans: C

least expensive sandwich exceeded $13 & most expensive sandwich exceeded $18

so, price must be greater than 4*13 + 18= 70

amarprajapati92 · Answer

Price of 5 sandwich exceed 70 let x1,x2,x3,x4,x5 be the price of each sandwich , that means sum of x1,x2,x3,x4,x5 >70

1). Least expensive is 13 , lets say all are 14 than 14*5=70 No, if lets say all 5 than 15*5=75 yes - Not sufficient 
2) Most expensive is 18, no idea of price of other 4 sandwiches -Not sufficient 
1+2 combined 
Lest expensive =13 and most expensive= 18 
That means other three will be in between 13 & 18 
14<15<16<17<18 = 75 sufficient 
Ans is C

catinabox · Answer

The question mentions that the price of the least/most expensive sandwich exceeds 13/18 dollars. Just because the price exceeds a certain amount does not mean that any of the friends actually purchased the least/most expensive sandwich. 
Lets say all the friends purchase the least expensive sandwich, the sum would be >65, if they all purchase the most expensive sandwich, the sum would be >90.
Answer should be E in that case.

pratiksha1998 · Answer

I completely agree with the above explanation and that's why I marked E since we are not told that the friends bought different valued sandwich. Are we supposed to make such assumptions in Data Sufficiency?  Bunuel

Bunuel · Answer

I agree; it would have been better if it stated:

(1) The least expensive sandwich bought by the friends cost more than $13.
(2) The most expensive sandwich bought by the friends cost more than $18.

At a restaurant, five friends each purchased a sandwich. Did the sum

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GMAT Data Sufficiency (DS) Questions

At a restaurant, five friends each purchased a sandwich. Did the sum

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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