Please explain this mongodb query and its result - mongodb

Question

The query goes as follows
db.restaurants.find({$and : [{"grades.score" : {$gt:80}},{"grades.score" : {$lt:100}}]})
it was written with the idea in mind of retrieving restaurants with a score of 80 to 100
why does this query return the following document in its result. the below document does not have any grade element in the grades sub-document which falls in the range of "greater than 80 AND less than 100".
i have tried using this
{
"_id" : ObjectId("572eb5df1d739cc73c21fab1"),
"address" : {
"building" : "65",
"coord" : [
-73.9782725,
40.7624022
],
"street" : "West 54 Street",
"zipcode" : "10019"
},
"borough" : "Manhattan",
"cuisine" : "American ",
"grades" : [
{
"date" : ISODate("2014-08-22T00:00:00Z"),
"grade" : "A",
"score" : 11
},
{
"date" : ISODate("2014-03-28T00:00:00Z"),
"grade" : "C",
"score" : 131
},
{
"date" : ISODate("2013-09-25T00:00:00Z"),
"grade" : "A",
"score" : 11
},
{
"date" : ISODate("2013-04-08T00:00:00Z"),
"grade" : "B",
"score" : 25
},
{
"date" : ISODate("2012-10-15T00:00:00Z"),
"grade" : "A",
"score" : 11
},
{
"date" : ISODate("2011-10-19T00:00:00Z"),
"grade" : "A",
"score" : 13
}
],
"name" : "Murals On 54/Randolphs'S",
"restaurant_id" : "40372466"
}

Answer 1

This happens because both conditions are true. When you don't specify indices for grades.score it search through all elements of the array. And it does find an item with score > 80 (which is 131). At the same time there exist other items that are less then 100.
In human language you request "a document that contains score greater then 80 and at the same time contains score less then 100". You don't specify that it should be the same score that satisfy these conditions.
What you're looking for I guess is a query for simultaneously checking range for each element.
{ "grades" : { $elemMatch: { score: { $gt:80, $lt:100 } } } }

Answer 2

Yeah as said by #Kirill Slatin, your both conditions are true in that case. So, for your required result, check out the following solution with an explanation for your better understanding:
Using $lte and $gte separately,
db.products.find({score:{$gt:'80'}})
db.products.find({score:{$lt:'100'}})
First statement will return the result with score of 80 and gretaer than 80 and Second statement will return the score results with 100 and less than 100
Using $lt and $gt together
db.products.find({score:{$gt:80,$lt:100}})
The above Query will return the score results greater than 80 and less than 100